I'd suggest using buckram or even Fosshape. I've never made a hat before though, so I can't recommend a pattern for that particular shape.
Fayt Leingod - Star Ocean: Till the End of Time - 90% finished
Morrigan (Winter Palace) - Dragon Age: Inquisition - 90% finished
Fidel Camuze - Star Ocean: Integrity and Faithlessness - 30% finished (on hold)