Only time my hat has blown off it ended up in my footwell as the airflow was from behind then forward as it swirled over the screen.
You could also get a small clip set to anchor the hat to your collar. A short cord with spring grips on either end.
I have a choice of hats from flat cap to baseball to trapper or peaked waterproof with fold down flaps.
I have a straw hat with chinstrap too....great in hot sun.
