I use water to stick down the paper and water as a cutting fluid on the
surface of the paper as I sharpen, the paper will last longer than using
it dry, this is messy while sharpening but cleanup is nothing more than
wiping up with a rag.
Due to their small size, I can see carving gouges being harder on the
abrasives.
I use marble floor tiles for the surface, one for each grit, as long as
the tool is wiped between grits there is no danger of contaminating
the finer finer grits. Granite is better, marble is never absolutely
flat where it has veining and if heavily veined will fall apart if kept
wet for extended periods, it was just what I had on hand and never
bothered to use anything else.
None of this is critical of your way, just the way I do it.
basilisk