From
How to Clean Everything by Alma Chesnut Moore
Keep straw hats well brushed and they will be damaged less if caught in the rain.
To clean a straw hat:
Wipe with a cloth dipped in warm suds, made with a synthetic detergent or soap.
Rinse with a cloth wrung out of plain water.
Note: Do not get a straw hat too wet or it may shrink.
Limp Straws
Limp straws can be stiffened by brushing them over with a light coat of clear shellac, diluted with an equal amount of alcohol.
To brighten the color and renew the gloss of dark straws, rub them with a dark cloth dampened with alcohol, diluted with one quarter the amount of water, then polish them lightly with a piece of dark-colored velvet.