Simply select any character with a non-standard head (I used a Minotaur, but this should also work with the Ogre, for example), and give them a hat or hair. Doing this will overwrite the "accessory" that is the non-standard head, leaving you with the disabled standard head beneath.

Congratulations! You now have an invisible head that will remain so for as long as you don't change the head part, which you can accessorise as you see fit.