This hat needs Jock'd.

[Benning Boy]

No need to go all Druid on the bonnet, just throw it in a sink with some lukewarm water and let it soak a bit. Then lay it on a bath towel, roll it up tight and wring out excess water. Put it on and shape it and wear it until dry, or nearly so. If you want to speed things up, use a hair dryer. When done you can use a sweater shaver, or whatever they are called, and shave the fuzz of the bonnet, leaving a nice smooth finish.

Of course, many of The Lairds like to wear their bonnets Pizza Boy fashion, I guess it's traditional, so if you don't do much to the bonnet, you'll be OK