I have taken bunny, squirrel, partridge,..and such other edible's,... with .22LR and/or .22magnum revolvers,...32 S&W Long and/or .32 H&R magnum,..and with a .357's using .38 Special, 148 gr Wadcutters. Never messed up all that much meat with those .38's.....
When I carry one gun to "do it all" out on the trail, ....I want it to "do it ALL",.....and it's usually been either a 3 inch, 5 shot J frame .38, or a 4 inch K frame sized .357,...though I would consider a Ruger Blackhawk in .357 quite capable of filling that bill as well, ..with the appropriate ammunition for the purpose at hand.
Having said that, I often carry a Ruger Super Blackhawk in .44 magnum,.... it all depends on the likelihood of sharing the trail or a campsite with critters that have the ability to chew on me,...or otherwise do me harm,....but I don't generally hunt small game with that one.
Personally,...If I am in back country with anything smaller that a .357 in the holster,..it's usually because I have a shotgun or rifle with me as well. I would NOT generally rely on a .22 or .17 caliber anything for SD,.... if I had a choice of anything bigger.
I have done a pretty fair amount of back packing by the way. I do not carry it IN the pack if I can avoid doing so. I generally open carry,... crossdraw when wearing the pack,...and when the pack comes off,..the revolver goes on me.
On those occasions I really don't want to alarm folks,....I carry crossdraw INSIDE an external cargo pouch worn on the waist belt of the pack. Line it with foam rubber to break up the print,..and you are good to go. I have modified the pouch I use to have a velcro tear open instead of using a zipper. Do make sure you are legal to carry concealed if you do this. That goes for carrying inside the pack as well. Check the laws in the areas you intend to travel,...some places even inside the pack and unloaded would still be considered concealed. If No CCW/CPL/CHL....I'd carry it for the world to see if it were legal. And last,..if I couldn't do that,..I probably wouldn't travel there.
Find what works for you,..and enjoy the trail!
The preceeding is just my 2 cents worth.....and your thinkin' may be different,..but hey,...each to them's own,....