hammertime,
From the museum bows photo's that I've looked at, it looks like grip wrapping was a personal thing (like here in the Great Lakes) the Eskimo paddle bows did not have wraps because of having to tension the cable. Some of the North Western tribes had some with and some without.....here's a couple of pics from the Peabody..... suppose you could do it either way and be "right".
One other thing is that the ones that were wrapped, it was usually with leather thongs, rawhide thongs or plant cordage....even if there was trade cloth under the wrap. At least on the ones I've looked at.....hope that helps ya some.
rich