Was it a rotten, stinky egg that actually exploded? Or was it just an egg that broke?
If it's normal egg goo, and doesn't stink, leave it, it'll rub off under the hen in a day or two. If it smells bad, it's full of bacteria, wash them. I just use warm water and dish soap, it'll come off easier than you think. I use an old knee-high nylon stocking to wash eggs, just rough enough to remove goo, soft enough not to damage the shell.
I have done this many, many, many, times, sometimes repeatedly if there was a lot of nest traffic or a clumsy hen, one bunch got washed at least five times during incubation. There were 6 eggs left by the hatch date, and 5 of them hatched. The last couple of times I washed them, I thought they were a lost cause and didn't even bring them back to the house so I'd have warm water. Just washed them under the cold water at the coop faucet. Stuck them back under the hen. Then they hatched.
Later, with other eggs, I discovered that dried egg rubs off pretty quickly under the hen, and quit washing them unless they smell bad. I just remove soiled nest material and put in new clean straw, and stick the eggs right back under mom. Those hatch fine, too.
As I've said a bunch of times, these eggs are not nearly as fragile as we think.
I have about 36 chicks running around right now, to prove it.
