A 6.5tw 22 CM will have no problem stabilizing any 22 cal bullet on the market. Now, will they all make it to the target before they fly apart, not likely.
That's a lot of twist in a cartridge capable of some pretty high velocities, particularly, with the lighter bullet weights so with light bullets you could easily be well over 400,000 RPM which is a sh$t ton. I don't know many bullets, except maybe solids, that'll hold together spinning them that fast.
With that fast of a twist If you want to shoot lighter bullet weights I'd probably talk to some of the places like Cutting Edge or Barnes that offer lead free and lathe turned solid copper bullets. Hell, even with 80 grainers you'll probably be around 350,000+ so the solids may be your only option.