I thought about Berg’s second option too, making hat+hair together. But if you put that in the same menu as the other hairs, it may cause problem with tiara slot.
A third menu point for hat+hair would make too many buttons in the face menu.
Or… Can you put it into the colourable hair slot? Can you change only the hair colour with the slider and leave the hats colour the same? That wouldn’t limit the choices so much.