For the razors that are in active use, I just dry it with as square of Tp (not touching the edge) and then I strop on linen (20x) and leather (40-60x) after a shave and that's it. They're stored open on a high shelf in the library/music room.
The ones that are not being actively used are stored with a coating of mineral oil in a box after being stropped several times.
I live on the NE coast of the USA. It can be humid in the summer, but it isn't usually too bad, and I'm far enough away from the coast that the salt spray is not an issue. In the winter, with the dry heat in the house, nothing is going to rust.
I lived in Ireland for quite a while (in my pre-wetshaving days), and if I was still there, I'd oil all my razor blades. I lived on the banks of the Shannon, and boy, was it ever humid!!
What I'm saying is that post-shave treatment of a razor really does depend on many factors (climate, season, use, etc.).