i would worry about a using a damp cloth on a foam surround or a paper cone. canaan is more than likely right, but its just something i would not risk.
Damp cloth. Most cleaners have chemicals in them that will smear the ink (if not a sticker) on the cone. A damp paper towel followed by a dry one has always worked well for me. I've used interior detail wipes too, but after it was clean just to shine things up. The down side to that is that many cleaners leave a film that makes dust stick to it worse.