Looks great! Both of mine are more beat up. I think you'd be OK just applying the tung oil with 0000 steel wool as an application pad, not "pre-scuffing". Just be sure to use 100% pure tung oil, and NOT some "tung oil finish" product. There's a big difference. The 100% pure TO might be hard to find, if you don't have some already.
I'd take the rifle apart though, and get the insides of the stock all oiled up too, and let it soak in real good. The steel wool should help scrub off any grime on the outside areas, and the wood should soak up the oil on its own. Might not hurt to set it out in the sun to heat the wood up and open the pores a tad.
Be careful not to leave any steel wool "whiskers" snagged anywhere, they'll make rust stains later. I'd use a little brush on the inside areas to slather the oil around.
Wipe off the excess after it's had a good soaking-in, and be careful with any oil-soaked rags! If tossed in a pile they'll generate heat and spontaneously combust (burst into flames). Spread them out flat to dry or put them into a metal container with a lid.
