If you cut at the right time (not too early) you shouldn't have much of an issue with keeping them moist. We only cut flaps, that close back together for the most part, and keep the moisture in, but by the time we cut, we usually have heads poking out by the next day, and everyone is out of the egg a day or two later, with yolk absorbed.

I've heard of people using saline solution, distilled water, or even straight tapwater.