DH has a Stetson Crushable that was bought 3 and a half years ago. He has worn it almost every day since. It has been ran over, dropped in mud, and a lot of other hard times but it is still there just not as pretty. He got a new one this summer on our trip and wears that one for good only, the old hat is still on his head most days and is still holding its shape just like the day he bought it.
My current favorite hat is a Style-master by Akubra Hats of Australia. It's a pinch brim Fedora and is made of 100% fur felt, but is not rigid and stiff like western hats. It is capable of bending and folding, but would I pack in into a suitcase?.... no way.
I've got several boonies, wide brims and narrow brims .... they are probably my first choice. Just make sure when you go wide brimmed boonie that it has side snaps and a cinch string to hold it on in the wind or when riding or whatever.
But I've also got an oiled Filson ... rollable. (See picture below) The oiled crushables are the high end of the niche imho. Winter time and I'm never caught without my Filson.
I wore a beret through all of my service years, long before everyone got to wear berets. We rolled them and stuck them in our cargo pockets. I still do it with my crushable hats and it works better than stuffing or crushing, just fwiw. But a beret, especially in cold weather, is something to consider.
I know you said you were looking for a cowboy style hat, but boonie hats come in lots of different colors, and not all of them have the "commando" look about them. I tend to like the OD green ones, but they also make them in tan, black, and Navy blue to name a few.I have several of them and really like them when it is really sunny or raining especially when working outside or hiking.
They can be easily crushed to fit into tight spaces of a pack and quickly retake their shape. When they get dirty from several days of wearing and sweating in them, they are washable by hand and will retain their original shape after dry.