.22 shot cartridges are a bit light on penetration. Good for sparrows out to about 15 FEET. Then-local chicken pen had a little problem with small birds getting in and raiding the chicken feed... Farther away and their feathers stop too many of the tiny pellets, and the pattern gets really thin. All this is from a rifle.
Have killed probably only three snakes myself, but from what I've observed digging non-poisonous ones out of the car's A/C system and other hiding places, a BB or pellet gun of reasonable power will do for any head or neck/spine shot. Can't recommend anything for gut-shooting them, based on what I've seen of runover snakes and those others have beaned with rocks. I just don't know if 450 fps inside of 10-15 feet is enough power.
.22 shot cartridges, I'd use them only out to 10 feet but no closer than 5 with a clear path to jump back. No feathers to act like a ballistic vest, but for poisonous ones the stakes are a bit high and they CAN move surprisingly fast even when injured.