Times like this a spray can of carb cleaner and a spray can of Brake-kleen degreaser (along with the little spray tubes that attach to the finger nozzles come in handy.  I'd remove the wood first, and work in a well ventilated area.  Some compressed air cans would be nice to blow out the cleaning stuff and blow in some CLP. Gloves.
However, every now and then a complete stripping is a needed thing.  Good luck.