How to wash & dry a wool Balmoral cap?

[unixken]

The headband of my wool Balmoral hat wicked up quite a bit of perspiration and body salts last weekend, and I'd like to launder the hat.

I suspect the best way is probably hand washing in the sink, lots of cool water, mild soap, rinse well, shape the hat, and let it air dry without wringing it out. I have a steamer to touch up any wrinkles later. Would that be the way to launder the hat? If not, is there a better/safer way to clean my hat? What's the best way to shape the hat while it dries?

Thanks in advance!