Ok, I got a bit impatient. I have some Matt black automotive vinyl wrap, so I cut a piece, stuck in on the watch, heated with a heat gun to get its shape (scary), then used a sharp x-acto knife to cut around the button. Not bad for my first try, one corner is a little messed up, but for now, I think it will work. It will be interesting to see how well it sticks over time. Maybe if I get a chance, I’ll see if I can fix that corner (I may have to start over).
If you do this yourself (you can buy a few sheets of automotive wrap on Amazon)- be Very Careful with the heat gun. You don’t want to overdo it and crack the screen, or somehow damage the watch.