Not a lot on the FL about cleaning straw. Can you soak a Milan straw hat in water and Woolite? (And reshape it afterwards?)
I did find this advice on ebay:
98. Cleaning Straw Hats With Oxalic Acid.—Hats made of milan, hemp, panama, and rough straw braids in natural colors may be cleaned by using a weak solution of oxalic acid.
To prepare an oxalic solution sufficiently strong for a badly sunburnt hat, dissolve 1 tablespoonful of oxalic acid in 1 pint of water, a process that will require from 15 to 20 minutes. When the acid is dissolved completely, pour 1 teaspoonful of the solution on a clean pine board. If it foams, or forms bubbles, it is too strong and should be weakened. Add more water and test the solution again. As soon as it fails to foam, it is of the correct strength.
99. While cleaning a hat by this method, do not put the hands in the acid solution. Use a small white-bristle scrubbing brush and scrub the hat quickly, beginning at the center of the crown and rubbing around and around until the side crown is reached; then continue around the side crown and on to the brim, rubbing the brush in a circle and in the same direction all the time.
Rinse the straw quickly with clean water, using the same brush for this purpose. Place the hat in the air or in the sunlight so that it will dry. The work must be done quickly in order that the straw may not become too damp and puff up. When the hat is perfectly dry, press it into shape under a damp cloth, using a hot iron. The ironing board used for this purpose should be heavily padded and the pressing should be done very lightly; otherwise, the imprint of the iron will flatten the straw. The damp cloth used should be lintless, if possible.
100. Cleaning Men's Straw Hats With Salts of Lemon.—Straw hats may be cleaned in a solution of 1 tablespoonful of salts of lemon to 1/2 pint of water. Dissolve by boiling, and after the solution cools apply to the hat with a firm brush, starting at the top. Dry with a soft cloth. Do not allow this cleaner to touch the sweat band, as it will harden the leather.
I did find this advice on ebay:
98. Cleaning Straw Hats With Oxalic Acid.—Hats made of milan, hemp, panama, and rough straw braids in natural colors may be cleaned by using a weak solution of oxalic acid.
To prepare an oxalic solution sufficiently strong for a badly sunburnt hat, dissolve 1 tablespoonful of oxalic acid in 1 pint of water, a process that will require from 15 to 20 minutes. When the acid is dissolved completely, pour 1 teaspoonful of the solution on a clean pine board. If it foams, or forms bubbles, it is too strong and should be weakened. Add more water and test the solution again. As soon as it fails to foam, it is of the correct strength.
99. While cleaning a hat by this method, do not put the hands in the acid solution. Use a small white-bristle scrubbing brush and scrub the hat quickly, beginning at the center of the crown and rubbing around and around until the side crown is reached; then continue around the side crown and on to the brim, rubbing the brush in a circle and in the same direction all the time.
Rinse the straw quickly with clean water, using the same brush for this purpose. Place the hat in the air or in the sunlight so that it will dry. The work must be done quickly in order that the straw may not become too damp and puff up. When the hat is perfectly dry, press it into shape under a damp cloth, using a hot iron. The ironing board used for this purpose should be heavily padded and the pressing should be done very lightly; otherwise, the imprint of the iron will flatten the straw. The damp cloth used should be lintless, if possible.
100. Cleaning Men's Straw Hats With Salts of Lemon.—Straw hats may be cleaned in a solution of 1 tablespoonful of salts of lemon to 1/2 pint of water. Dissolve by boiling, and after the solution cools apply to the hat with a firm brush, starting at the top. Dry with a soft cloth. Do not allow this cleaner to touch the sweat band, as it will harden the leather.