I wouldnt count on a 2" .357 doing much to a bear, I real cant say wether or not it would wollup a bad kitty. I just dont think it has enough of a barrel. Just empty the cylinder into the critter

. I could be wrong, its just a guess.
I bet it would have a stiff recoil, but I dont think it would be painfull. Like you said, you can practice with .38s. When you need the .357, I doubt you would be worring about recoil.
How much does the S&W 360 weigh?
Im a skinny guy myself. I think wearing the proper garment, and a well fiting holster goes a long way.
If there was a snuby .357 on the rack when I got my .38. I would have got the .357 instead of the .38. Just make sure its stainless.