The paper towel trick won’t work to get oil off of water, I’ve tried. Works fantastic to get water out of oil, though. A paper towel will choose water over oil every time.
I’m a pro painter, and countless times my nitwit helpers have tried thinning alkyd (oil) paint with water, thinking alkyd (oil) based paint is the same as acrylic (water) based paint. Touch a corner of a paper towel to the water and it’ll shoot up into the towel almost instantly. The oil will stay behind.
Not sure if it’s a viscosity thing or what, but it works well for me.