Antique Straw Sun Hats

I recently aquired these 2 unusual shaped straw hats from an elderly lady. She said they were in her family for years...but she couldn't remember their origin. I have a large collection of vintage straw hats but nothing like these! The best I could come up with was that they could be African as I saw a pic of an African worker in the 1920's wearing something slightly similar. I feel like the ball on the top has some signifigance but no idea what!
Anyone have some knowledge they would care to share?? Thank you in advance~