If you have egg on your face, your Charisma is temporarily and sharply reduced, lasting until either you get hit by or immersed in water or #wipe with a towel. This could also apply to having cream pie on your face.

A possible addition is for monsters to throw random (non-cockatrice) eggs at you.

Another possible addition is to add a new “egg trap”, which fires eggs at you with the intention of getting egg on you.