I was just going to suggest something like that too but honestly I think it would also cut down on his ventilation. Maybe he could buy the hat but cut out the center portion leaving only the front visor and rear flap. BTW: I found getting a helmet with a visor helped a good deal but sun screen on the tops of my cheeks; back of neck and thighs has been very important. You can probably jury rig a rear flap of some kind. Or just grow your hair long in the bacK!

I use some head sweats but maybe there is a headsweat that has a wide tail?