I was just fretting about this the other day..
I have my hands down by my sides, but then start thinking that they look too "straight" or don't know what to do with my hands. So I cross my arms. But then I think that I must look awkward, with my arms crossed in a weird fashion. Or maybe I look like I'm not a very open person (body language). So I grab my phone and fiddle with it, or light a smoke.. but then, eventually, there's nothing to do with the phone, or I finish the cigarette. So in the pockets they go. But then I worry that having my hands in my pockets looks sketch, or that I look fat because it makes my jacket poof out a bit at the stomach. So I put them down by my sides...
Lol. It's definitely a confidence issue. I'm sure no one really gives a shit what my arms/hands look like. Try relaxing in public, maybe by focusing on other things going on, or by breathing calmly. If you're waiting somewhere where there are seats, sit down and place your hands in your lap so they don't feel like they're just hanging there uselessly.
Even better.. instead of walking, ride a bike around! Your hands will be chillin on the handles, you'll look like a badass, and you'll get around places faster. Like a boss. %)