Greetings Nartker,
I've had a foldable leather hat from Barmah Hats for years.
http://www.barmahhats.com.au/
It has a broad brim that keeps sun off, is made of leather to offer a little
protection from 'stray flies' and can take a beating.
My own hat is about 10 years old and apart from fading considerably is as
good as ever. It has been worn continuously for five years in the outback of
Australia and survived a further 2 years backpacking around the world. It
has been dumped in the water, fresh and salt, but has never lost it's shape.
I've thought of replacing it, but who wants to part with an old friend.