I usually skin 'em out, flesh it and put it on green. When it dries, it will shrink some and be molded to the shape of the handle.
I'm afraid once it dries out, you may not be able to do much with it.
I will tell ya not to thin the edges too much though. Beaver tail is not very tough. The lacing holes will tear out very easily, especially if their too close to the edge.