I wear a nylon fishing ball cap with mesh side panels.
A while back, I bought one of those Bug-Off brand bandannas that are impregnated with the Permethrin.

Mine had a button hole on one corner, and a button on the corner diagonally across from it. I assume it was for securing around the neck.

In a flash of out of the box " genius" ::), I decided to convert it into a Doo-Rag/ Sunshade for my hat.
I swapped the little button for a large coat sized one, and on the button hole side, I took a small stretchy pony tail scrunchies and looped it thru button hole and sewed it secure. Rather than tying a know to secure it, I just button it up. The stretch in the scrunchie loop, keeps it secure and comfortable.

Now I have bug/sunscreen to wear under my ball cap that still allows the mesh hat panels to breath but if the little no-see-um get thru, the can't bite my head/ears/neck area. I can also wear it sans hat, something I usually do on portages, as I always seem to be knocking the hat off or it gets skewed on my head in a most annoying fashion :P
It's long enough on the perimeter to protect my neck from sun and when I dunk them both, the cooling effect is really noticeable.
All in all a idea that really worked as I envisioned ;)