I rinse while shaving and use face cloths to wipe the blade down. I bought a dozen or so at Target, They're specifically for my razors, so SWMBO doesn't get angry if I cut them. I tend to be a sloppy shaver, so when I'm finished, I give the blade a good rinse, then wipe it down with a dry hand towel. I use the corner of the towel to wipe out the area by the pivot pin.
I also give the razor a good shake when I'm done, just like you'd do a brush (Yes, You need to be careful doing that) The blade stays out overnight on a paper towel, then gets wiped down with a silicone treated cloth.
I like the idea of the oil and alcohol. I see a jar of it in my future. Every once in a while, All my blades get treated with Renaissance wax. It's good protectant. This may be a bit anal, but Florida's bad.