I bought a leather hat as you describe Bloomer. It was from an agricultural show from a stall selling hats made by 'The Australian Bush Hat Co.' (label inside says 'International Hat Co.'). Needed a lot of leather treatment to get it waterproof but was only £20. Has some loops inside so you could fit a neck string. But mine is a snug fit and hasn't blown off yet. Worth spending a lot of time trying them for fit. The salesman said they do shrink slightly when they get wet and dry out. They do, but only very very slightly, like just a few mm.