Hi Charlie
With any cellulosic fibre, you will always run the risk of cellulosic browning if the dampness isn't even all over. Your proposed technique should, with care, work OK though, but practice beforehand.
If you were to add a steamer to your proposed technique (wrap several towels around the head and wipe down with this rather than using a dry folded towel) you will achieve a superior finish and even dampness that dries just as, if not more, quickly.
Make sure that your Onestep Fineline sprays out as a
fine mist and not as droplets or a jet.
Safe and happy cleaning

Ken