SkyDancer,
For many years, treed cougar were killed with .22 Long Rifle guns. Cougar skulls are actually rather fragile and the .22 was used to make sure that the cougar’s skull was not shattered such that it could not be boiled, cleaned of tissue, and then set on a desk.
Body shots are another matter.
PS Having a pack of dogs as a backup did make such a light cartridge less risky than it may appear at first reading.
When we’re up in the hill country (dense forest here) we carry a 30-30 and/or a .45 carbine using hydra-shocks.