Yup, any soft cloth may work, just try them all out.. paper towels, a sponge, a dish towel, a baby diaper cloth.. you can spritz the cloth with water if you want, or alcohol.
I've never done this, but I have heard some people soak the soap bars in water for a few seconds to clean them.
I can't remember where I picked this tip up but I use Knee high hose to buff and remove ash. I usually sit with a spray bottle of water and spritz and buff. It also is nice to use just to add a shine to your bars.