For close shots the 20 Guage will work the best and do less pelt/hide damage...you'd be better off getting a .22 Magnum,.17 HMR or .17 Fireball,.22 Hornet,.204 or .223 with a light bullet in 35-40 or 55 grain!

As Johnwb82 mentioned....maybe the .410 with a slug to reach out further?The .22LR with say the CCI Stinger Hollow Points but thats pushing it and You may have several run off unless You have a Semi-Automatic and get 2 or 3 shots off?