I used to oil my blades before putting them away, but got annoyed having to clean them up before shaving with them. Now I just leave the razor open leaning with the spine and toe against the razor coffin until dry and then put them away.

If I’ve been sloppy during the shave, I run some toilet paper between the scales to make sure all the moisture and any excess lather have been removed and that the pivot end is dry and clean.