You can use whatever you want, but shot smaller than #6 tends to just make a mess, unless you are shooting them for pest control and not eating. #6 is fine, but #4 usually cleanly penetrates and will knock them out of the crotch of a tree.
Been a lotta years since I went squirrel hunting with a shotgun. But back then, the best places were stands of very mature hickory and oak. Start to do the Pythagorean theory (remember geometry class ??) on a shot to the top of a 75 foot tree that's 20 yards or more out.......... Now you're looking at a 30+ yard shot and squirrels can tend to cling tightly to life if not hit in the head.
I usually used #5 shot as a good and happy medium.
