Do you have a sample of what a "rare" specimen hat looks like? Are you looking for fitted Thai historical hats or plain old ball caps? Provide a link.
No problem finding ball caps for sale. Phetchaburi Road, mini garment center, near Baiyoke Hotels will have many clothing vendors - some with hats. You will find street vendors selling hats on Sukhumvit Road, not far from Nana Skytrain stop, and in Patpong area. These are mostly ball cap types. Many places here and there you will find small shops with hats for sale. Even in malls, usually sporting departments, you will find hats.