For upkeep,,most any quality oil or grease sold for firearms maint. Keep it simple, it's just a metal finish you're trying to protect from corrosion. It's pretty tough in itself compared to other blues and the usual matte type finish holds protective coatings well.
Don't try to (re)invent a special oil for the task. There's no need.

I used WD-40 as a quick spray down/soak on fresh rust blued bbls and parts for quite a while in the past.
It was the water displacing property I was taking advantage of,,but it's already noted quirk of taking some of the new RB off made me stop using it.

Now after the wash down to clear the surfaces of any residue that may cause after-rust, I let them dry of their own heat from the hot soap & water/rinse used,,, wiping any obvious excess off of course.

While still warm I coat with a thin coat of Linseed oil,,same artist type drying Linseed Oil I use to top off a stock finish.
They hang for a day or so and any excess is wiped clear of the metal. An ultra thin coating is left, nothing you can really feel. It drys because it's so thin.
On top of this goes a coating of the favorite of the moment oil or grease during re-assembly.

Better looking bluing, no break down of the finish and no after rust. Just my experience.