Does the hickory stave need a raw hide backing? Unless it is a board with bad violations or grain runoffs it shouldn't need a backing.
You can add rawhide to a stave that is held in reflex but it is not going to change the performance of the bow any. Hide glue is probably the best glue for rawhide because they are both made of the same substance.
I see you are in NY. How is the humidity there? Hickory, rawhide and hide glue are all very hygroscopic, meaning they take of moisture as the humidity climbs. Even with a good finish the bow will be real soft during high humidity times. A self bow, even hickory, fends better in high humidity than a rawhide or sinew backed bow will so if not needed a backing can be detrimental.