The best is deer rawhide as it is very thin, light and strong. The dog chews are cattle hide, which is thick. As mentioned above if you use a chew it has to be sanded quite a bit to thin.
If you have privy to road killed deer and a place to soak in a wood ash/water combination to dehair and strech hang the skin you will have rawhide in a very little while.
Have any goats around for a hide, that would be good, too.
I agree with the titebond 3 glue. It holds it very well.