D.N.
You can use alcohol without damaging the wood, just don't rub it too hard. One thing I have also done is use a hair dryer to heat up the residue. It makes it a bit easier to peel off the heaviest and then alcohol to get off the remaining. I used this on our doors because a tenant let his daughter put stickets all over the door.
One thing to watch for it what type of varnish is on the wood. If it is a natural wood finish, anything oily could leave marks.