Wet mounting is not without its conservation problems, either.
It is not in the nature of skins to stay flat. You can flatten them (search here under 'humidity chamber" and then look for 'papyrus'), or send them out to be flattened; not an expensive treatment, but drying time is two weeks. An 8 ply window mat should be used, covering as good a portion of the document. There should be at least 1 1/2 inches between the edge of the document and the rabbet of the frame to allow for expansion and contraction. Skins are very susceptible to changes in RH, and even in a sealed mat package they will move and wrinkle over time. The good thing about not wet mounting them, but hinging them (top only, with fewer, wider hinges) is that they are easy to remove to be worked on when the time comes. Which it will.