I had snow white shoelaces on a pair of brand new sneakers, but Nature wasn't having it and they're splattered green and brown by now. I tried washing laces before in soap and water, but they tend to become "fuzzy", stretch, and gradually fall apart. What would be the best way to clean them out without stretching, damaging, or ruining them?
The easier something is to do, the more likely you'll do it. If it's quick, so much the better.
Treat the laces as you would other easily damaged (delicate) garments. Put them in a mesh bag to reduce the wear-and-tear of the wash cycle.
Keep them clean as you would your white trousers. Don't wait until they become stained and grimy. Periodically, remove 'em, bag 'em, wash 'em, and dry 'em.