Why don't you just stick to 'standard velocity' ammo? That's what my 39A shoots the most accurately.
The 22LR is a fairly low pressure round anyway. I can't see a problem with it. I know our metallurgy has come a long way since then, but typically the chamber area and lock up of the lever guns is very sturdy and thick. I can't see a 22 busting a barrel open as long as the bullet has somewhere to go.
I might stay away from 'hyper velocity' rounds to error on the side of safety. I really don't think high velocity rounds would be a problem.