Well, no not in the traditional sense, like the Stetson Cattleman style, which I prefer. But here's a few examples that are like Cain's 'cowboy hat'.
So as you can see Cain's 'cowboy' hat is very similar to the above styles and Rush may be correct.
Justin 4X Aspen Fur Felt Western Hat
Stetson Bozeman Wool Felt Cowboy Hat
Stetson Sturgis pinchfront
(A traveling cowboy's crushable Stetson hat)
Sheplers.com has scores of hats like these (plus Boots, Shirts, Jeans, etc.) and where I 'have to' shop. Unlike you in Texas (or and Western State) there aren't any 'western' clothing stores in the Chicago Metro area (that are safe for gringos anyway). Even the Tony Lama boot stores that used to be here are all gone. So I get my boots at Sheplers too.
Check them out. Maybe the prices are better than any local stores near you. And their Customer Service is tops.