I usually just find a clean spot on the rag, drape the rag over my index finger at that point, grab the bottom half of the rag with the rest of the fingers on that hand, then pull the top half of the rag over my arm in the opposite direction of the object I need to wipe. Everything out of the way and you have finger point precision. I usually use a rag the size of a t shirt. Takes a little practice to be comfortable with it, but it's likely no harder than fishing out wipes! Either way, I'd agree, something to wipe with is the one tool (apart from brush and roller) that I use all the time to keep cut lines neat.
I just have a wet rag that I leave draped out of the way over the braces of my step ladder. If I make a little oopsie, I reach down and grab it to clean up. It stays wet enough to use for hours, and it's reusable. Do you use the wet wipes like that, or for something else?
Sorry folks, country's closed. Moose out front shoulda told ya.