Super glue. It was designed for bonding to skin.
Okay. Seriously now, you're looking for a kind that ties under the chin. The problem you MAY find, is that your son is serious about not wearing hats. If this is the case, what you are going to have is a screaming, fit throwing, red faced little boy who would rather choke himself with the string then wear a hat. Can you tell we did that? Oy.
If that turns out to be the case, you have two options: Cross your eyes and bear it until he cries himself out and gives up... or: Use sunscreen.
We use the really expensive spray kind from city peoples, because my husband is a redhead. (Hmmm...what option did we go with?) No rubbing. Just mist, air dry (about 3 seconds), and go. SPF 50. On hair and everything.
Of course, the very next year our son wanted to be "like daddy". So as long as daddy wore a hat, he would, too.
Sigh. Oh well.