I needed baby wipes and was still really set on making this work. I finally got the paper towels I planned to try to use instead of napkins.
The towels all seemed sufficiently moist.
I removed the cardboard bit in the center.
Once the diaper was changed I asked him how the wipes worked. He said that they were useable but they still fell apart a bit. When I asked him if they fell apart more or less than the ones you buy at the store he said more.