I hunt my squirrels in the mountains in either oaks or sugar pines. I like to use .22lr, 40 gr solids. In some areas, you're better off with a shottie do not always knowing what's behind your target..... shooting up into trees.
I just drive to my hunt area, get out and quietly stroll thru the trees, often standing or sitting perfectly still for a while. I look for signs and listen for them barking.
I always gut and clean mine, put them in baggies, then in an ice chest before I leave the mountains.