Well, I'm sure you can have trodes styled as a hat. It seems like something that has to be possible, I mean, I can't see people walking around in public with just a net on their head and not trying to find a way to make it look more appealing.
I wouldn't give the "hat" capacity though; I'd treat it as a slightly more expensive version of the trodes. It's just tropes "in the shape" of a stylish hat. It'd still probably be recognizably trodes (your hat would have a data port, for one) upon even just a knowing glance, but I don't think it'd seem out of place at all.