There are a lot of sunscreens that aren't greasy & smelly. The newer stick stuff with zinc comes immediately to mind...
In regards to the need, regardless of anecdotal comments to the contrary I know the sun isn't good for the skin, I'm fair skinned, light eyed and burn quickly so I avoid it as much as possible.
In regards to fishing shady places, 10+ years ago some of my favorite creeks WERE 98% shady until the ash, hemlock and other trees started dying. As a result, some pools that used be shady are now bathed in sun for most of their length at different times of the day.
When I come up on one of those spots and know I am going to be out in the sun for an hour or so, I'll roll down the sleeves on my fishing shirt and apply some sunscreen to exposed skin.
In regards to dorky fashion statements, as much as I chuckle at Tilly or Updowner hats,...
I used to wear one of these as my fishing hat:
Hoo boy, thank goodness I never went the tweed jacket route...
😳