Here's a method an old timer I met showed me once. He showed me with a rabbit but I have done it on squirles and other small game too.

Cut a slit in the skin across the middle of the back, do not cut into the meat though just the skin. make sure the cut goes the entire width of the back or it doesn't work as good.

next, pull the skin away from the meat with your fingers around where you made the cut. Get your four fingers in under the hide with yout thumbs on the outside of the skin - Your hands should be like if you were to make a fist with both hands and put them together in front of you with the knuckles together and top of hands pointed upward. then just act as if you were trying to turn the skin inside out. Once it is pretty much inside out cut off the four feet, tail, and head.

Doing it this way you will have no hair on the meat and it gan be done in under 5 minutes -

Remove inards after the animal is skinned.