I have a Lowe Alpine mountain cap - GoreTex and fleece, with a baseball peak and earflaps. Great in cold weather, earflaps reduce buffeting, peak acts as sunvisor. Stays on at 80mph with the top open. Doesn't look too naff. Earflaps turned up in warmer weather - in hot weather, Musto sailing (baseball-ish) cap instead.

Being follicularly challenged, I too wish to avoid skin cancers.

Nigel