On wood such as that where it is very thin, it is pretty easy. Take paper towels and wet them. Make them so they are not dripping water, but also holding a bit of water. Fold them in half and and lay them on the outside of the stock. Use the typical housewife iron and iron like you would anything else. Iron until the paper towels begin to turn brown. Get new towels and repeat over all of wood. The paper towels will be dry when the turn brown. The steam you create will do a couple of things. It will bring dents out of the wood and it will dry the wood out by forcing oils out. When your steaming the wood from the outside, it will collect some oil in the paper towels and it will force oil through the thinner wood and it will collect in the barrel channel in the form of a greasy substance, much like vasoline. I did this not two weeks ago on an enfeid musket from the mid 1800's. It worked great. One last thing, DO NOT SAND unless you really have to. Hope this is a help to you and good luck.
mdrim13