How to Clean a Wool Fedora Hat and Sweatband

If you perspire heavily while wearing the hat, carefully wipe down the inside and outside of the hat with a damp cloth to remove excess body salts. Turn the hatband out and allow the hat to dry completely between wearings. If salt stains form on the felt, dip a white cloth into an equal mix of distilled white vinegar and water. Spot clean the salt stains and then allow to dry completely. Use a soft brush to restore the nap of the felt.

If the sweatband is made of leather and it becomes stiff, clean with saddle soap and then use a leather conditioner to keep it supple. Take extra care to prevent the conditioner from touching the felt because it will leave a stain.

To remove oily stains from hair products, lotions, or body oils, sprinkle the stained area with cornstarch or talcum powder. Allow the powder to remain on the hat for at least a couple of hours and then brush away. The powder will absorb the oils. Repeat if the stain remains.

Do not use liquid cleaners on the hat unless the fibers are synthetic. You can use a bit of mild detergent mixed with water on a clean, white cloth to spot-treat stains. Rinse by wiping with a cloth dipped in plain water and allow to dry naturally.

The Spruce / Cristina Tudor

Hat Care

• Store your fedora in a covered hat box or on a covered head form to prevent dust from settling onto the hat. Store upside down to prevent the brim from becoming misshapen.
• If you must pack your hat during traveling, stuff the crown with clean socks or soft underwear. Create a hat-sized nest inside the suitcase and place the hat, crown down, into the nest making sure the brim is not creased.
• To help preserve the shape of a fedora, always grasp it by the brim. Make sure your hands are as clean as possible each time you touch the hat. Even with clean hands, the oils from your fingertips can discolor the felt of your hat over time. If you handle a fedora by the pinch of the crown (the pinch is the part of the hat where all of the fabric comes together to create a point), this can create a rip in the fabric, or cause the pinch to become asymmetrical.
• If your hat gets crushed, place it on a hat form or over a rounded jar. Use a handheld clothing steamer or hold over a kettle of boiling water to steam the hat until slightly damp. Reshape the hat to the original condition and allow to air dry away from direct heat.

• If you decide that your felt hat needs to be dyed to refresh the color or you'd like to change the color, contact a professional dry cleaner that specializes in the care of leather and/or offers dyeing services. 

source: https://www.thespruce.com/clean-a-fedora-hat-and-sweatband-2146407