Hey Dave,
Squirrels are the "toughest" skinned small game in my neck of the woods. Their hide really is pretty tough. A pellet, .22 or .177, can and does of course penetrate it but it's definitely tough. A rabbit on the other hand is just the opposite. Their skin is very soft, probably one of the easiest small game animals to skin for the same reason. The only other animal I can think of that is really pretty tough skinned, small game wise, is a woodchuck.
As for a material that could be placed in front of the putty to simulate skin I had a thought,,,, how about one of those "chamois" cloths (don't know if I spelled that right) ? You know,,, one of those thin leather like sheets that you use to wipe the residual water off your car after you wash it so you don't have water bead marks or streaks on your car? They are available at any auto parts store or Walmart, etc. They would be easy to place and secure in front of, or over, the putty you're shooting into, and they are relatively cheap. Not quite sure how such a material would hold up to repeated shots, but it might work.
I don't know, it was just a thought, what do ya think?
Jeff