There are mildew killers that are not Hydrogen Peroxide or Sodium Hydroxide based, and are claimed not to bleach any materials. They are usually for garden use, and are supposed to kill but not remove the mildew. My guess (and it is a guess) would be that that and a scrub would be the way to go.

Bodad's suggestion of a drycleaner's is good. They use chemicals to spot-clean mildew.