A can of compresed air, a pkg of Photo Wipes (brand name) and either Edwal or Kodak Anti Static Film Cleaner. Remove the slides from their mounts, one at a time. Use the compressed air to blow off the heavy, solid bits and pieces on each side. The Photo Wipes are a soft, lint free paper towel designed for cleaning negs and slides. Soak part of it with the film cleaner and gently, very gently clean both sides of the slides by wiping them with the wet Photo Wipe. Neer, as in NEVER us a photo wipe dry! They will scratch. The film cleaner with very slight finger pressure will take most anything off, but be careful to blow off the solid particles to prevent scratching. Now remount with plastic mounts.
I've used this system for cleaning negs and chromes for about 25 years and have never scratched any of the film. This will take some time, but it's something that can not be rushed and will do the job.