My sis-in-law uses those thin cleaning cloths (like for wetting down and wiping a sink, but not a sponge). You can buy them at the cleaning aisle of the supermarket in most countries (I can't remember the brand name in the US... but they have narrow pale blue and white stripes... made of some material that doesn't fray).
They come in packs of about 4-8 large cloths and she cuts each one into maybe 4-ish smaller ones for use as baby wipes. They launder fine and dry quickly (I also used this exact same system for awhile with my oldest child, in fact - just dampen the dry cloth with water from a squeeze bottle and use cloth to wipe baby. I stacked mine up in a cute basket next to baby's change table, and then each one would go into the laundry basket after use). The advantage is that they are very cheap and easy to create. If some get too stained through the wash after years of use, you can always throw those ones out then and make a few more.
Hope this helps... if you are interested in this let me know and I can try to look up the brand next time I'm in the supermarket.