TYREE
If I am not mistaken, that bow was probably made in the '60's, if not the '50's. If it has held together this long, why would you think it will come apart now.
Snakeskins really make a bow look good. However, your bow is a real piece of archery history and in my opinion should be left original. As a true collector's item it has a certain collector's value. If you add snakeskins you will hurt the value.
If you have to have a snakeskin backed bow, please do it on something else.
Just my thoughts, but it is your bow to do with what you will.