apologies for a necro-thread, was searching for something around the same time (August or so of 2017, that thread coming in a few).
But I did dye the hat a month or two ago and it turned out great.
Picked up some RitDye from ACMoore (yes, it's at WM, but with the coupons that ACM or Hobby Lobby etc put out, I WOULD have saved a bit on the same product in my local WM.
But I went a different direction, using the powder form.
It was simple to use and did the trick well!
The hat has a bit of a pattern on it, almost like a chevron pattern - zig zags.
Well, even after the dying, there was still the pattern visible, so that was cool.
Appreciate the above guy who suggested the dye!