Whatever backing you choose to use, I would suggest to only use one strip. Multiple layers of cloth, paper, etc. will not give extra strength, it will only add unwanted weight to the limbs, slowing down the bow's action.
Personally, I would go with a silk or linen backing, then shoot the crap out of the bow like Pat says. Then, when you are sure its a keeper, do the snake skin, or- you could paint a snake pattern on the backing, and save the snake skin for a really nice wood selfbow (I am assuming red oak board, you didn't mention).
Just a thought.
Mike