dude, you shoot a stick with a stick!
what kind of adhesive you using? If it were me, i'd use epoxy and just go right overtop of the rawhide, if the rawhide is good and flat...if you cut it, you'll have a hell of a time making it all perfectly matched up, and you'll probably have to bind the ends of the rawhide for 2 reasons: keep it down, and hide the unsightly end of it. It you have epoxy, you'll be fine.
What! 8 guys and none of them knows what to do? El Destructo, what do we do about these guys? lol