Have you thought of a bandana? :d I used to wear one when cycling; no need now helmet 100% sun protection. I was thinking of wearing one for running; however, i tend to run early morning and the sun isn't as strong so may not need one
ive got an Inov8 hot peak cap, its does the job well, lets my skin breath as far as i can tell, but im not bald and so am only really going by how sweaty my hair gets (not perticually). Not sure about UV stuff, am sure it will tell you on the website.