If you have a centerfire handgun for defense and you just want a survival gun for small game, consider an air pistol with a detachable or folding stock.
For the intended purpose, it would be as good and in some cases have an advantage. If you start with a high quality, powerful air pistol like a Sheridan pump or the new Browning magnum springer you can reliably take rabit, squirrel or pigeon. The advantages to an airgun are less legal hassles and less noise. Just having a firearm can be arrestable in many situations where a pellet gun would either be OK or just ignored. You can have a short barrel and folding stock on an airgun with no SBR legal hassles because airguns aren't considerd 'firearms' by the Fed legal definition of the word. That lets you get more compact than you can practically do with a 'real' gun. The low noise and small package make it possable to bag a critter where you may not want to advertise your presence or actions.
During the depression my grandfather used a Benjamin Franklin pump pistol to bag game while he was roaming around the country with his mother. In the country, no problem, just hunt. In a city park, be discreet... and hunt. That was then, this is now, but yesterday's lessons still hold true. He favored an air pistol because he could hide it from bigger kids or from any adults.
A better gun isn't better when it gets taken away. A 22 is better than a pellet gun, unless you can't have a firearm........