I want to share my simple discreet alternative. Though my fedora rarely comes off even in high winds this stops it getting away - which is much more comfortable than trying to stop it coming off.
you will need:
A narrow bootlace that approximately matches your hair colour,
A small brass keyfob - the type that hotels use - basically a thin brass disk about 3/4" in diameter with a hole near the edge.
A small metal button with a largeish loop on the back - rather than a flat button with holes through it.
Needle and thread.
Keeping the plastic ferule at one end of the bootlace, cut off enough lace to go half way round your head.
Poke about half an inch of the cut end through the hole in the keyfob.
Fold it back on the rest of the lace and sew it in place. Stitch it so the lace stays as flat as possible.
Flip the hat's sweatband up.
from the inside, at the back of the hat, work the lace's ferule carefully between the stitches that hold the sweatband to the hat.
pull the lace all the way through until the keyfob stops it.
flip the sweatband back in. The keyfob doesn't show, you wont notice it's there when you wear the hat.
Put the ferule end of the lace through the loop in the metal button and tie a knot to stop it coming out again.
Next time you don your hat the lace will hang down the back.
Bring it round the side of your neck tuck it inside your shirt collar and put the button through the top button hole from the inside.
The lace hardly shows as it runs round the inside of your collar.
If you don't regularly wear shirts you could make the lace longer to reach a jacket buttonhole. Or replace the button with a small strong clip.
If you use a decorative button it looks like a Masonic shirt stud.
If you usually wear a tie make the lace long enough to reach the second hole from the top of your shirt and put it through from the inside. your tie will hide it.
Those factory installed things just flat don't work now. 
