When I do wipe my hands during sharpening, I always have 2 or 3 yellow microfiber towels at hand while doing so. They're large enough and absorbent enough to mop everything up, so my grip doesn't get too slippery while working. These are the microfiber towels you'd see in bulk packaging at places like Costco or Walmart (maybe Sam's Club), marketed for auto detailing/buffing/waxing, etc. They work well and last a
long time; I'm still working through a package I bought probably 20 years ago, maybe longer. They'll come out of the laundry still looking very dirty from all the swarf they've collected, but that's also a testament to how well they pick that stuff up, when wiping down the stones. As dirty as they look after laundering, they still do the job.
I've mentioned here before, my hands get extremely dry & cracked in my locale (desert southwest of USA), especially in the winter. When my hands get all oily during my sharpening sessions, I EMBRACE the relief. When not actually sharpening knives with my oilstones, I rely heavily on mineral oil-based hand lotion to keep them from getting too dry. So, I'm gettin' oiled one way or another, and I welcome it.

I realized a long time ago, even with the mineral oil-based hand lotion, simple washing of the hands with most any decent soap & warm water will quickly wash away the traces of it from my hands. Same with the mineral oil I use for sharpening. So, when it's time to clean up, it's very easy. Liquid dish detergent is even more effective, in warm water.
When my knives get very oily during a sharpening session, I'll take that as an opportunity (sometimes) to give them a bath in dish soap & warm water, when I'm finished. Rinse in HOT water, so the residual moisture evaporates off easily, and re-lube as needed.