What are you using to glue the rawhide down? I've typicallybuse Titebond II, and I usually wait two days. If using hide glue, the 7-10 days may be necessary depending on your climate, longer if more humid, but I'm sure someone here has more experience with the rawhide hideglue combo.
If your handle isn't bending, butting the rawhide will work fine, you can thin it out a bit and overlap if you want. Definitely overlap if a bending handle bow. This may not be necessary,and probably overkill, but for protection, I run a bead of superglue at the end where the two overlap, on the piece that is on top.