This reminds me of one of my best friends, and hunting buddy. He was the worst squirrel cleaner ever. I used to kid him, that I couldn't tell which squirrels he had cleaned, they were all covered in hair!
I never found the perfect answer, and I tried several cleaning methods. Basically, just go slow, and try to keep the skin away from the meat. As a final cleaning, I would scrub the meat with a stiff brush under running water. The squirrels I clean in the field are either in a stream or pond, where I can keep my hands and the meat reasonably well washed. I finally decided, the meat I gain from squirrel hunting isn't worth the effort, and I have quit hunting them. I ended up with various small game and birds in the freezer, never getting eaten. I put everything in a slow cooker with some veggies, and even my wife declared it almost edible, high praise from her. But I digress, good luck with your squirrel cleaning.
