I have carried various SAKs in sweat-soaked pockets over the years, including overnight and multiple days in a row, and nary a spot of rust. I would be absolutely shocked if one rusted from a single night in some sweaty shorts.
However, I have seen Vic scissors build up “gunk” (this is the appropriate technical term) near the pivot like that, fouling the action. It was able to be scraped off. I would start with a fingernail, but not hesitate to move up to something metal.
Please let us know how it goes!