If you can't get cotton cord thin enough to go through the holes and thick enough to "scrub" the inside, you might try that "fluffy" dental floss. (I think it's a Johnson & Johnson product called "Reach" gentle gum care floss.) It's sort of stretchy, but it might be hard to thread through the bead holes because it's also very soft.
Thornton Floss
http://www.thorntonfloss.com/ might be a better choice because it has a stiffer section that could act like a needle, and a soft "fluffy" section that could scrub.