I don't know, the hat looks more "country farmer" than "intimidating gunslinger" in that poster, maybe they should have cut off the top of his head instead of the arm.
Looks to me like a regular Stetson cowboy-style hat.
Getting off-topic for a moment, but all this talk about billing reminds me of the compromise for the two leading stars of The Towering Inferno
Note the names are in alphabetical order left-to-right, but Newman's name is higher, so neither star could claim "top billing." Actors and their egos . . .