If you want a hat of a similar shape, I can’t tell the actual material of this hat but it looks like it might be leather? The hat I personally can recommend is a harvested wild Kangaroo leather hat. They are foldable and crushable, you can put them in a bag and then when you pop them open and shake them out they go right back into shape. I love mine and wear it daily for K9 Search and Rescue work in the very hot western state in the US where I live. You can also water proof them with leather wax, and mine looks better than the day I bought it. It comes in different colors and styles but here’s the one I personally have:
https://www.amazon.com/Barmah-Hats-Vintage-Kangaroo-Leather/dp/B00P483SXY/ref=mp_s_a_1_5?crid=10HD9IAGOQ53N&keywords=barmah+hats+for+men&qid=1666155426&qu=eyJxc2MiOiI2LjAxIiwicXNhIjoiNS4xOCIsInFzcCI6IjQuNTMifQ%3D%3D&sprefix=barmah+... I bought the Barmah because my husband loves his so much. I also wanted a cool looking but very durable and practical hat I didn’t have to care for, and I fold this one up to travel with it. I also customized the hat band by removing it and having my own attached, and putting a feather in it. Hope you find a great hat for your needs!