Both wipe his hands on the towel and with the towel are correct. In the first instance the towel is passive ( maybe it is hanging on a hook) and your hands are wiped on it. In the second example the towel is active. He has picked up the towel and is wiping it over his hands. Both are commonly used. And wipe is also an appropriate word you use. Alternatively you could use mop, clean or dry. They have a slightly different meaning to eachother and to wipe but may be used in the same context. Eg he.mopped up the spill with a towel. Eg he dried his hands on the towel Eg. He cleaned up the mess with the towel.