Make your own reusable swiffer cover! I am lazy and I just use an old washcloth and shove it in the holes. Microfiber cloths are good for dry mopping wood, and old wash cloths squeezed to remove most of the water are remarkable for mopping wood.
ONLY use this and it leaves floor spotless. (Heavy duty floor cleaner recipe: ¼ cup white vinegar 1 tablespoon liquid dish soap ¼ cup baking soda 2 gallons tap water, very warm.) It leaves everything smelling amazing.