Ah, sticky duct tape, that's a good point. That stuff does seem to sweat out its adhesive. Maybe stick with higher quality "gaffer's tape"? But that stuff is pretty spendy, and if you go cheap on it, you're probably liable to basically be back to regular duct tape. Good luck with adhesive vinyl!

Another idea: maybe cut a t-shirt into like 2" or 3" wide strips, and wrap like a mummy? Secure ends with staples? Or how about papier mache? Hell, you could make an entire skullcap out of papier mache! It would be hella light. Make a frame out of pipe cleaners or other flexible wire? Depends on how much energy you want to expend in order to achieve nothing.