I've cleaned my chalks a couple times. Did washing machine method once & just toothbrush/soap & water method the second time.
The only difference between cleaning the wool and regular UBs is that you need to be a little more gentle with the toothbrush on the wools since cleaning will leave them looking a little fuzzier than before. Scrubbing in just one direction is a good idea. The weave goes in all directions though so just pick one and stick with it.
You could also pretreat the stain with shout or something like that before you scrub.
No matter what, the fuzziness around the tip of the toebox will increase a bit after cleaning, I took a fabric shaver to em though and they're good as new.