I used a damp paper towel (used distilled water) folded in half and gently draped over the top of the eggs to keep them moist after I cut. Not dripping damp, wetted and then wrung out damp, it worked nicely.
I noticed with mine (was my first clutch this year, so am far from expert) that when I checked and the veins were looking brown (I assume it's because they're no longer supplying the baby and clotting up) that I'd find that baby out of the egg on it's own roughly 12 hours later.