On topic:
You need to wash the salt off before oiling.
Simply drying and oiling doesn't do much to remove the salt(s).
Not necessarily on topic, but...
Add another carry gun (or three) to the lineup.
Give the sweaty 'piece' an extra 24 hours to dry after your initial wipe-down, and it may help with the rust. As is, you may be sealing in moisture and salt with the daily oiling.
And the problem may be the holster, more than drying.
I have three standard carry pieces (all IWB):
LCP
LCR (.327)
P95 (blued, 9mm)
All Rugers, and two of them are blackened stainless, at that. But their particular finishes are not important.
The LCP rides in a leather holster that sucks up moisture like a sponge. It can take 3-4 days to dry the holster after a hot day. If the pistol wasn't mostly plastic and stainless, there would be big problems in keeping that as a daily carry. Though it's difficult to wash leather without some complications, this holster really needs it. The salt just keeps building up in it.
The LCR rides in a Remora (nearly) all-rubber holster. While nearly "impervious" to sweat, moisture does still find its way inside the holster. I have to separate the holster and revolver after a warm day, so that each can dry thoroughly. As I type this, the revolver is in the safe and the holster is drying on my work bench (day 2).
And the P95 is, unfortunately, currently in a cheap neoprene holster, A.K.A.: sweat sponge. Though the holster dries fairly quickly, drying it out doesn't remove the salt. Repeated use turns the holster into a nasty salt lick that's just more and more concentrated with each use. The holster has to be washed, to be cleaned adequately. And drying it after a good washing requires at least a day - especially since the P95 is blued steel (not stainless) and has plenty of nooks and crannies to trap moisture as my warm body 'pushes' moisture from the holster to the relatively cooler pistol.
And if, for some reason, all of the above are currently unusable at the same time, due to wet holsters or some other factor, there's always something else I can carry temporarily...
(In my case, it's usually a derringer for CC, or I go big and OC a .44 Mag if the day's activities will allow it.)