I don' think it is necessary to use a positive and negative mold to clamp the leather between. Hat-makers have for many decades been doing what you want to do with just the block method. Either a plastic, wood, or DIY'd block should work.
I agree with footrat, finishing the underside of the brim will raise the look of the hat considerably. Also, in the photo you posted there is stitching showing at the base of the crown. I'm not sure if that is a design element in itself or the maker stitched a sweatband on the inside. You may want to craft a type of hatband to cover any stitching that is done.