No one should take chances with skin cancer. With skin exposed to the sun without protection of sun screen or shade, we are doing just that! What we didn't know about that in the past can sure come back and bite us! Both of us have at least one or more pre-cancerous lesions that have to be removed at every six months check-up with the dermatologist.
It is much worse when young people have to lose part of their nose, for instance. It is amazing how well that can be repaired with part of an earlobe, though.
Maybe you haven't found the right shape of straw hat. I'll bet there is someone at Youngs' Western Wear in Valentine who could help you find the right fit. I do fault western straw hats for not having enough ventilation. But you can get additional metal grommets put into them. At least I was able to 'retrofit' my old hat, found in a second hand store in Tombstone, with them. Got it done in one of the booths at Cheyenne Frontier Days a couple of years ago. Also had a stampede string put in so I wouldn't lose it in our SD winds. I use it mostly for yard work, and the rare outdoor event where we are not under a grandstand. Styles with ventilation woven into the crown look like they would be the least hot.
Or, you could go the way I saw a guy a few days ago: it appeared to be a terrycloth kitchen dish towel under his baseball cap hanging down all around the sides and back covering his ears and back of his neck. I'll bet it soaked up the sweat that would otherwise have been running down his neck, too.
Seriously, I sure hope you find some tolerable shade soon.
mrj