Mike, I believe it's the sodium hydroxide or lye which would be corrosive. I think the wood ashes would be pretty much inert, but it would probably be best to experiment on a junk piece of wood before doing a stock from a good gun. I have many times used household ammonia to clean grunge from dirty stocks because the ammonia will also saponify old gun and skin oils and the resulting soap is water soluble. Works great and I've never had any rusting issues with the metal in wood cleaned that way.
I do know though, that I'll be saving some wood ash from the fireplace for oil spots on the garage floor or driveway. When I saw how well it sucked up the oil spot on my garage floor, my immediate thought was how well it might work on an oiled gun stock.
