I tried shaving my head completely bald the other week, but the dark areas where the hair still grows are really obvious so I can't get away with it. And believe me I've tried hot towels, 5 blade razors, the works.

since losing all my hair to AU I always wear wigs when out of the house i.e., at work.  When out hiking I've developed my own head cover with an old wig that I've cut out and put a scarf/bandana over it. and also when skiing i wear an old wig under a helmet.  At home the first things I do is rip that horrible thing off and enjoy having nothing on my head at all or I wear a buff when it's a bit cool.