I'm trying to make Cicero's hat look like it does on male characters (no head wrap), but on a female character. Is there any way to do that?

yes, you would have to change the female model of Cicero's hat to the male model so that both genders point to the male model of his hat. You can do this by editing Cicero's hat in the Creation Kit. When you open it up there should be model paths for both male and female, copy the path from the male model and past it in the female path. However, keep in mind the male hat might look weird on females or maybe even clip since it wasn't made for them.

Would be better to CLONE the hat FIRST.

Then make the changes to the clone, as Steez says above

Yeah, like h4ent says above, you should probably make a copy of the hat before you do this so you can avoid any conflicts.