Nice looking old gun and my guess would be beech, if you look at both sides of the tang there seems to be those small "tigers" typical of beech.
Keep in mind that the plainer the gun the less attempt to match anything so the forearm could be something else. --- John
Yes, I think the forearm is walnut. The forearm is just the spring snap on type so I was wondering if they might have used walnut for it as it has to take the stress of being pulled on to remove as well as house the forend iron and barrel pivot. I'm thinking money was saved by using a cheaper type of wood for the stock. As far as coloring, they managed to get the two looking pretty close and patina seems to be about the same making me think they are from the same time.
One thing for certain is that it is a very petite gun built on a 28 gauge frame.