You might try placing a damp rag over the rawhide backing and see if it will swell a little. this may eliminate the clamp marks.
When I add any backing(rawhide, snake skins, etc) I will wrap it with cloth strips(Ace bandage works too) but only for an hour or so until the glue bewgins to set. After that I remove the wrap and trim the excess backing with a sharp razor. I also check for air and excess glue pockets and if found I make a small slit, lengthwise to the limbs, in the backing and squeeze out the air or excess glue.
There is no need to add clamps to a cloth or skin backing.