I THINK when he' in disguise if I remember. Am I misremembering?
That would be Commodore Schmidlapp and he's still wearing a hat -- a captain's hat.
I don't think he's even seen not wearing some hat. Even when he fights and gets punched it stays on -- hence the chin strap.
Anyway, I'm sure several people are googling right now to see if he ever was shown without a hat.