Cleaning and eliminating stains in Shantung

[WizardOfBoz]

I have a Stetson that's a bit of a Frankenhat. "Genuine Shantung 8x". Classic style (crease and pinches on both sides, 4 inch brim, brim turned up on sides, and down in front and back), more cream colored than pure white. Three ventilation gussets (terminology) on each side, turquoise (!) in color. I've added a brown woven leather Stetson hatband, of the "Belt loop" style, with little silver medallions spaced around the hat.

Quite wearable, but there are brown stains around the sweatband, near the vent gussets, and where one grabs the hat (in the pinces) to take it off. Kind of yellowing.

Is there any remedy for this light staining? Is this oil getting into the shantung, or salt, or...? Thanks!