I've used Rem Oil on the bluing to prevent rust ... seems to work fine. I use to use Birchwood Casey "Sheath" many years ago, which also worked well for blueing. Searching Amazon and the 'net, I don't see Sheath anywhere, so it might not even be made anymore.
Update - more searching ... it looks like "Sheath" might now be called Birchwood Casey "Barricade".
Rem oil is extremely light, I find it works fine but it seems to need refreshing a bit earlier than other lubes. I did see an interesting video in crazy low temps the Rem oil performed much better than some other favorites.