Mime Mask

The Clothier only lists it while a Blood Moon is running, which is the same night his town is being taken apart. That means the purchase happens with something chewing on the door. Either give him a room that cannot be reached from the ground, or spend the night thinning the wave and buy just before dawn.

Blood Moons come around often enough that missing one costs nothing. There is no reason to fight a losing defense over a hat.

It is pure costume and sits in the social helmet slot, so it covers your real headgear without giving up the defense. Among the faces the Clothier carries it is one of the few that lands closer to unsettling than to silly, which is most of why it gets worn.