"Would you prefer me to wear a hat or not wear a hat?"

Like others have said, many ways to express it. Do/would you prefer me wearing the hat ? Do/would you prefer me wearing the hat, or not ? Should I wear a hat ? Should I wear a hat, or not ?

I think there are a few different ways to say it. 1. Do you prefer me to wear the hat or not? 2. Do you prefer that I wear the hat or not? 3. Do your prefer me wearing the hat or not? We use "to" when talking about a choice between two things ("I prefer coffee to tea"), but your example is more of a either-or question which doesn't need the "prefer one to the other" structure.

Do you prefer if I wear the hat or not?

Voce prefere que eu use chapeu ou nao?