My dermatologist said he "loves" (insert sarcasm here) ball caps. They miss the ears and he removes so much cancer from the top of ears he buys a new car every year. If you have the neck thingie and that covers the ears great! If you're ears aren't covered then get them covered.
As a side note he too suggested that having a beard with the lifestyle I'm living it a good thing. Great Sun protection. A little bit o' a pain diving but I've learned to live with it. Rather keep my lip cancer free then take the risk.
Ciao