You want to clean up the stock too. That cosmo can leach out of the stock and into/onto the metals, so you're best off by cleaning it up too. I put it in the black garbage bag, wrapped the stock in paper towels. and let it sit outside a day down here. Then I applied hot water/simplegreen to clean it up. Did a bit of heat gun stuff, but I didn't feel comfortable with that. Here's how the stock sat at that point.
It wasn't bad, but I knew it still had some cosmo in it - it felt odd, and greasy. Did NOT like it.
So then I switched to turpentine to clean it up.
THAT got it out.
I then applied some military wax I got at Home Page
. 1/3 beeswax, 1/3 boiled linseed oil, and 1/3 turpentine. It cleaned it more (applied with 0000 steel wool) and I let it harden up. Then I wiped it all down and hand applied the stuff again and let it absorb.
Here's how it sits today.
It cleaned it so well, I can see stampings that I hadn't seen before.
I've used this process on my M1 Garand (1942 Springfield) and it came out wonderful.