I'd take a 22 because the ammo is cheap and light, you can reach out farther and it'll damage less meat. I must have killed thousands of small critters with a 22 growing up as a kid on our family farm - mostly rabbits and various rodents. I'd feel really comfortable feeding myself with a good 22 and iron sights in the scenario laid out by OP. On the flip side, a shotgun would be more versatile considering all the different types of ammunition you can run through it from bird shot all the way up to slugs for large game.