Deck restain after damage from paint spill 

You can try olive oil. Let it sit on the paint 60-90 minutes and wipe off. Many times it will take the paint with it.

I think your method is worth a try. I have removed paint from lots of different wood surfaces, and there is just no easy way without refinishing the wood. At least not if you want the best finish. The hand rub seems like low risk option for not doing too much damage.