I am a bit of a skins expert, I've done over 150 bows and you are absolutely right.
Never soak a bow. I should have been more detailed. The warm wet cloth or paper towel should be folded to cover only the skin, and only part of the limb at that. I usually use a paper towel and check it every time the towel gets cool. This keeps you checking the limb every ten to fifteen minutes or so. You will also be looking for the limb edges for any darkening showing moisture absorption. If you see this, simply stop and dry well with another paper towel. Since you are checking so often, not much will have seeped in and it should dry quickly. You can still continue to use the warm compress, just make sure you are applying just daMP AND WARM and drying /wiping edges often to keep it from getting into the wood lams. As the skin begins to loosen on the edges, you may be able to start peeling those skins right up.
If you see that you have a big issue with moisture getting into the edges easily, wipe them down with a paste wax before applying the moist cloth. This is easily removed later with turpentine lightly wiped over it.
Good call Dave, I was not paying attention.