I have used tung oil successfully on many shafts. A quality tung oil will leave a clear finish that is slick and very resistant to dirt, chalk and moisture. Tung oil, as most know, is most commonly used to treat teak trim on sailboats.
As for applying, be sure to clean and smooth the shaft, but do not burnish. Apply a very thin coat of tung oil (be sure it's pure tung oil and not something that includes polymers, say, tung oil plus polyurethane). Be sure to apply a thin coat. Too thick a coat will be must more difficult to rub off.
Allow the coating to dry at least a couple of hours, or better, overnight. Next, take a cotton rag and start rubbing. Tung oil is difficult to remove, so plan on expending some elbow grease.
But once you get the excess rubbed off, and polish the resulting finish, the shaft will become remarkably slick and the finish is very hard, very durable. The worst thing is, for a week or so, is the surface will be so hard and smooth, it will be slightly tacky until it get microscopically roughed up. I found using talc solved that pretty well.
The shaft will require minimal maintenence. All I've ever done since applying the finish is dampen a rag, wipe down the shaft, burnish and play. The shaft will be resistant to bluing.
I still have 4-5 shafts I have treated 20+ years ago and I've never done anything else to them. There is some yellowing, probably more than natural aging, but it's pretty slight and looks fine. It is not a strong yellow like linseed oil.
Be aware, tung oil in its liquid state is poisonous. Once it dries, that's not an issue.
I'm currently using Mike Gulyassy's "Shaft Freeze" for my new shafts. Mike lives close by, so it's easy for me to get him to treat my shafts. I would say Shaft Freeze does what tung oil does (clean, slick surface and protects the wood). I don't see much advantage one way or the other. But given that I am a lazy sort, it's worth $30 to pay Mike to do it.