Sounds like .22LR and .17HM2 are your only simple options. Personally, I wouldn't bother with the .17 as I don't see the benefit. Yes trajectory may be a bit flatter, but the bullet is too light and you get increased wind drift and downrange energy is pretty pathetic in practical terms at ranges where the flatter trajectory is of any use. Plus there are fewer ammo choices and its more expensive.

As for me, I have 3 rimfires, a .22LR biathlon match rifle, a .22LR that shoots subsonics for small game hunting and a .22WMR that one day I plan to experiment with barrel twist and reloading to use subsonic 60grain bullets. At the moment the latter is a beautiful 100+ yard rabit gun and closer range fox round. I won't be getting any .17s any time soon.

Just my 2pence worth... Have fun with your project whatever you choose!