Steam is your best friend when it comes to vintage hats. It doesn't matter if it comes from a professional clothes steamer or your tea kettle. Though I will admit the professional steamer is much more user friendly. Not only will it deodorize but it will rejuvenate and relax all of those wrinkles in a delicate veil, ribbon or floral trim. Try not to saturate the item completely and be sure the item that has been steamed has dried thoroughly before storing. While steam can be your BFF, the moisture left behind can be your worst enemy if it is left on the item. Moisture will cause the item to accumulate mold/mildew and can cause the material to decay. Felt and fabric hats respond best to steam. It has little to no effect on straw. If using on silk or satin, be very careful not to over saturate as it can cause water spots.
The only exception to this is fur. PLEASE DO NOT STEAM FUR. Especially vintage fur. Trust me, I learned this lesson the hard way. I was steaming a late 1800's fur lined cap to remove the wrinkles when the fur suddenly curled up and shrank before my eyes. There was absolutely nothing I could do to stop it or repair it. It was heartbreaking.
So the next time you see that perfect vintage hat but it looks a little wilted, remember your tea kettle.