I'm bumping up this old thread, because I found a source of cotton laces. I don't think they're 100% cotton, but they were exactly the laces I was looking for. These are the ones I used back in the day, they hold tight, don't slip and are gentler on the hands. They're made by Riedell, and below's the search image:
I can tell you where to get them in the MD/DC/VA area, but outside of that I can't help.