You can buy empty intact rubber stopper vials, I've done that (ordered them, possibly got them shipped from the US iirc). Then you can follow the method I described.
Don't heat it, it's not a reliable method and it's a bitch to boil a solution inside the vial with limited room for the pressure, even if you put in a needle as valve. You can technically sterilize an empty vial by boiling a long ass time and then fitting the valve needle with something like a cotton filter (in a syringe barrel) because it will draw in air as the temperature inside cools, you don't want that air to contaminate your vial again.
But then you'd still have to sterilize your K solution, by means of a micron filter.
I thought micron filters where not supposed to be used in the "drawing" direction, crOOk? Probably because they are composed of multi layer filters including a rougher pre-filter and a final membrane. You'd clog the membrane in the other direction? Messing too much with filters is not recommended because they are not perfect anyway and have some sort of tolerance to particles varying per particle size (like a spectrum). Fucking up your filter may make it tolerant again to particles defeating its purpose, if you force after clogging etc. Am a bit hazy on the details but from what I read about that I don't advise that kind of thing.
I have wondered about theoretically re-sterilizing used micron filters, assuming that enough heat would actually kill everything without melting the thermoharder material, or using a desinfectant or appropriate desinfecting solvent (which perhaps would have to be put in the reverse way to 'wash it out'). Never done it since it just seems sketchy, but I'm still interested to know why it wouldn't work.
And anyway crOOk, you'd have to repeat your method with like 10 syringes and switching the same filter each time to be able to accomodate say 10 ml as 10 doses. Other than those reasons it'd work.