Proper paint for straw hat

[DocSavage44]

Found the perfect straw western hat for a project I'm working on, but it is brown (painted) and needs to be black. Anybody out there have any recommendations for the best method and materials to paint the hat? I was thinking of using some sort of shoe dye, like Scuff Magic or Nu-Life spray.

I want something that will adhere and also not flake or rub off on my clothes and skin.

Thanks in advance for your assistance!

Cheers,
Doc