The idea of a ghoul wearing wig is most likely a reference to the ghoulish aliens in the John Carpenter movie, "They Live". Many of the "ghouls", as they are credited, have false hair very similar to this, as well as faces that are reminiscent of the Fallout ghouls.
If you confront Griffon while wearing one of the wigs, a dialogue option will come up where you can ask where he got his hair done, because it's the same style as yours. He'll respond by nervously agreeing.
If you shoot at a wig, it sounds like you are shooting an organic body part, and blood will spatter on the floor.