Is there a John Wayne movie out there where he didn't wear a hat of some sort?

Try The Quiet Man. He may have worn a hat in some scenes, but it’s not a cowboy or ranger hat for sure. He plays an ex-boxer, and it’s a great movie.

McQ? I don’t think that he wore a cowboy hat in that one.

Likely no hat in McQ, Brannigan, Greatest Story Ever Told, Circus Show, Hatari (probably a safari hat, though).
He played so many soldiers, sailors and cowboys it would be hard to find him sans hat in many films.
Also, remember that during his hey-day men wore hats so even if he’s not playing a cowboy or soldier he may still sport a hat of some sort.

I am referring to a hat of any kind, beret, cowboy, spanish conquistador, helmet, anything like that. Thanks for trying!