Well, thank goodness I was wrong about the "living" in the coop bit - it was just hiding from me there. I think. It departed the coop and my yard, tail held high in warning until it got to a spot it felt safe enough to lower its Stay Away flag whilst skuttling away.
Any other critter and I'd just bash the heck out of it with a two by four right there in the coop. When I first saw it IN the coop, I had turned on the light to make sure I could check on everybody. The skunk was standing on its hind feet, holding onto the bottommost tray of the roll-out nest unit. There was a broody banty hen in the nest just above that one, and she was WIDE awake, scrunched down so only her eyes and the top of her head was visible. She persists in setting there, even though the eggs roll away.....
My contractor friend reiterated his suggestion I buy a shotgun, especially for the new, not-yet-my property, which is in country visited by mountain lion, fox, coyote, bear and rattlesnakes.