Airsoft guns are not for hunting, they only shoot plastic shot. BB guns are for the most part not good for hunting either. Theres nothing like what you describe for the little money you're talking about. The Crosman 1077 is the closest thing, but has its problems. It isn't a BB gun, it shoots only pellets. BBs won't fit. If you aren't willing to load a single shot rifle, you most likely are not going to be willing to take the time to load the 12 shot rotary clips the 1077 uses.
I would say this if you want to hunt squirrels with an airgun- save up a bit more money, get a decent gun, learn to shoot it and practice so you can hit what you are shooting at. One shot is all it should take to drop a squirrel if you have a decent rifle and know how to use it. Killing squirrels with a barrage of poorly aimed low power BBs is a pretty inhumane way to hunt if you ask me.