What I settled on (gray one), best summer hat I've owned, strongly recommended. . . https://www.epochhats.com/shop/linen/cotton-fedora-hats-with-band-f2805.html
I've used a Tilly for many years. Started when I sailed south Florida and the Florida Keys in my 17' day-sailer (no sun protection in a day-sailer). For the past 20+ years it's been my favorite desert hat as I explore the deserts of SoCal. They last forever and are very comfortable. As a special bonus, I look dashing, especially with my new beard.
Most people don’t think about the top of their hands. I’ve had several spots frozen, and a few cancers cut off.