Two days ago I dispatched a 3 foot copperhead that had gotten into the dog run. My preferred snake gun is a .45 Colt SAA with CCI shotshells. I usually load 3 shot shells and 2 Federal 225 grain LHP. I've never had to resort to the LHPs. The first shot incapacitated the snake, the second decapitated it.
The smallest I would go is .38 Special shotshells. While .22LR shotshells might work, I just don't want to get that close (I really don't like snakes). I have plenty of reach with either the .38 or .45 shotshells.