Substitutes for Wet Wipes that Attach to a Mop
Use Washable Microfiber Cloths as Substitutes
I have used microfiber cloths as substitutes for disposable wet cloths. When one side is soiled, I turn the cloth over and use the other side. They can be tossed into the wash instead of thrown away. Ironically, one package of reusable microfiber cloths cost less than a package of disposable wet wipes for my mop. Substitutes are a better choice.
Baby Wipes are Cheaper than the Cleaning Variety
Sometimes disposable wet wipes are necessary, but the variety meant for cleaning floors are not a must. Substitutes can be used. The type used for cleaning the diaper area work just as well as those for the floor. I prefer organic varieties. Buy a large package of baby wipes in a variety of your choice. Thick substitutes work best with a mop designed for wet wipes. When in doubt, try one on a small inconspicuous area of the floor. If it will not harm the sensitive skin of a baby, it probably will not hurt the floor. Make certain that it will not streak before cleaning the entire surface.
Make Washable Wet Wipes with Organic Bamboo Fleece Material
Bamboo fleece is one of my favorite fabrics. I love it because it is organic, and it does not fray along the edges. It can be used to create countless no-sew crafts. I purchased one yard of white organic bamboo fleece, and I made dozens of washable substitutes for my mop. The material is 70% viscose bamboo and 30% organic cotton. My substitutes are highly absorbent, and even though the fabric costs around $11.50 a yard, it is still far cheaper than wet wipes that will end up in the trash after the very first use.
Source: Personal and Professional Home Design and Cleaning Experience