I ber that you could take some heavy non fusible pletex and make a cone pattern. Then take some fusible webbing or stitch witchery and iron the fabric to that, sew done the sides with the right sides together to make the hat. I would think that you would sew wide elastic or make an ajustable ribbon and sew the ends to the hat and embellish it as desired.
Sorry if this doesn't help you! Good Luck!