I would recommend, if you haven't already, looking at what accommodations in his environment may benefit him before going the route of medication, if he has trouble in a particular setting see if you can pinpoint why. Since he's older it may help a lot to talk to him directly about what things make it hard for him to focus or function and see if there are external things that can be adjusted to help make life easier for him even with his ADHD symptoms.
I was diagnosed with and treated for ADHD in childhood although in my case it was a misdiagnosis for what was really Autism Spectrum Disorder and the early signs of C-PTSD, that said there's a great deal of overlap between the symptoms of ADHD and ASD so non-medical accommodation could benefit him in either case. Many of the things that helped with my Autism related difficulties have actually been of great benefit to one of my boyfriend's who has ADHD and is trying very hard to get through college right now without any medication.
Some examples of what was offered to me in schools later in life that helped include the following
(Note that this will be long and I'm only going to list school based things to prevent it from being exceedingly long, but there are similar things you can offer him at home if that's where he faces more difficulty and I'd be happy to cover some of that if you'd like)
- Being permitted to switch between sitting in a chair and sitting on an exercise ball in class (so I wasn't forced to sit still all the time)
- Being permitted to chew gum in class (so I wouldn't try to meet my sensory needs by chewing inedible things and wouldn't be inclined to hurt myself by chewing on my hair, nails or skin)
- Being permitted to bring toys such as fidget cubes or stress balls to class and use them, or to doodle on paper or read a textbook while also listening to the teacher (Aside from meeting sensory needs I'm not sure why this helped but it made it much easier for me to focus on what was being taught, I suspect this is best for those who find visual input distracting and learn best through listening and not looking at the person who is speaking)
- Being permitted to sit in whatever part of the class made it easier for me to focus (I could sit in the front one day if I was having trouble hearing due to sensory processing issues, the back the next if the fluorescent lights in the front made it hard for me to focus/think and next to the door on the next day if my anxiety was severe and I wanted to know I had an escape route)
- Being permitted to wear noise cancelling headphones or hooded sweatshirts with the hood up in class (thus allowing me to block out some excess noise while still hearing the teacher)
- Being permitted to work on what would normally be randomly assigned group projects alone or with someone I knew and felt comfortable with (this meant I wasn't put at as high of a risk of severe social anxiety or bullying due to the differences in my social skills)
- Being permitted to take tests alone in quiet rooms with no time limits (lack of time limits reduced my anxiety and thus led to better academic performance, being able to do it alone in a quiet space prevented me from getting overstimulated or otherwise distracted by my environment)
- Having the questions on math tests rewritten to include things that interest me (I struggled to understand math after about 6th grade due to intellectual delays which created an immediate aversion to any math projects as they made me feel incompetent, by incorporating my hyper-fixation/special interest (animals) into word problems it made them less intimidating because they suddenly involved something I knew tons about and I became less likely to refuse to do my schoolwork as a result.)
I've also been told that during my late elementary school years (which for other psychological reasons I don't remember well) I was given the option to leave my class if I was becoming overstimulated and go to one of the first grade classrooms where I would assist the teacher with sorting homework into the cubbies of the students it belonged to or assist with other calm tasks while the kids had quiet time. I do know that this helped with just generally making school life less stressful for me by providing a calm place to escape to.
It may be good to ensure his teachers are aware he has ADHD if you haven't done that yet, sometimes this makes them more open to offering accommodation or helps with understanding why he might be struggling. When I was attempting to get through college the first thing I would do before enrolling in a class is email the professor explaining that I'm autistic and giving a brief summary of how that affects my behavior and abilities in a classroom. I found it helped immensely in creating understanding between me and my teachers. At this point I often preface many of my interactions with new people by saying "Hey just so you know I'm autistic and it affects me in the following ways (stimming in "strange" ways like hand flapping or rocking, not understanding social queues, getting anxious/upset in loud or bright environments etc.), please be understanding if I do something that seems odd to you and feel free to ask for an explanation once I seem to be feeling ok." That explanation alone leads to much more understanding relationships with people and lessens my anxiety about getting things "wrong" when in a social situation that may not otherwise be autistic friendly.
I'm afraid I'm not familiar with non-stimulant medication options for ADHD (much of what I was medicated with were stims) but I am happy to see you seeking them, stimulants can help ADHD but in other cases can also create new problems. And on the off chance your son is misdiagnosed and actually has autism or another developmental disorder with similar symptoms stimulants could even worsen his symptoms. I still feel in cases of developmental disorders accommodation is best, I know it can fail to help at times. And at other times like in my case the accommodations just can't be provided to the degree they're really needed. Even with everything I was offered my needs as an autistic child were never fully met and led to a great deal of difficulty functioning later on in life. In those situations sometimes meds are a good supplemental option, but I would definitely encourage avoidance of stimulants and trying to keep him on the lowest dose that can still help him.
Whatever you do please listen to him, if he doesn't like a medication try a different one. If he thinks a change to his environment would help then offer that to him. I know there's a pretty common implication out there that people with mental illnesses and other brain based disabilities aren't aware of what they really need and in some cases that may be true but I still feel the most helpful thing you can do is listen to what someone says they think would help, because they are the one that has to live with whatever's going on in their head on a daily basis and they are the one who has seen first-hand what does and doesn't help them.
Being medicated and seeing doctors from a young age was horribly traumatizing to me. I learned to see myself as a behavioral problem or a disease that needed to be drugged away. But the thing is that I was given no autonomy, I was given no space to say "I'm not ok with this treatment" and I was forced into being medicated and hospitalized and generally put through it all for most of my childhood and teenage years. All without a moment of feeling as if anyone actually cared about helping me, instead of just caring about making me an easy person for others to deal with. I'm not saying this to discourage you from medicating him by any means but rather to encourage you to involve him in any treatment you try for his ADHD, when you work with your son, his teachers, his doctors and any other family involved be sure your son never feels silenced by what others are suggesting. And do try to see meds as a supplement to creating an ADHD friendly environment in his life, not as a primary treatment for it.
So to sum up my incredibly long rambles (sorry, I didn't mean to write so much!) I am not certain what non-stimulant options are out there for ADHD however I'd imagine most psychiatrists would be happy to look into that for you, in my experience they really do prefer not to prescribe any substances with potential for abuse if they can avoid it. But in the meantime while you search for some medication that helps do see what things you can do to make his world an easier place to live in even with his ADHD. Work together with him on figuring out what he needs both in regards to accommodations and to medications and don't deny him the option of saying no to any treatment he's uncomfortable with. If he says no w/o even considering a treatment option gentle encouragement is ok but never force or coerce him into something he doesn't want.
Best of luck with whatever treatment path you take! I hope you can find something that helps him whether it be a medication, an alternative like therapy, an alternative like environmental modifications or some combination of the three.