When I restore a blade and re pin it I put washers in and cover the pin and pivot and washers with Evinrude marine anti corrosion grease. That stuff repels water and I've taken the lower unit of an outboard apart after two years under salt water with no water or corrosion in the bolts or fittings fittings. So I am not worried about water in the pivot. Grease beats oil but can't be added from outside. There are some great bicycle bearing greases as well.
Keep water away from your blade and you are good. Wipe the blade, don't douse it. When you hone be sparing with the water. It isn't really hard to keep water out of a pivot. E Almost every razor I've unpinned has had corrosion on the pivot, but almost every razor has also had terrible honing, uneven bevels, excessive wear at the point and often other damage. Take care of your gear and it will take care of you.
i oil my pivots with a small needle oilier i use 4 my firearms. it is refillable and i do so when needed with any oil i have on hand mostly fine machine oil.
SF bay area, oil the razor lightly if it is not going to be used for more than a week. This includes the pivot, and you should work to ensure that water does not get in there in the first place. If it does you need to get in there with a square of TP and get it out. Lightly oil the blade (I use mineral oil, but as others have discussed, there are a number of more "high tech" options available in gun loving countries. But get some barrier on there. The good thing about plain old mineral oil over the new gun protectants is that it is easily wiped off before use.
If this is your only razor, and you are using it every day, or every other day, I believe oiling is not an issue. As long as you take off the surface water after use, you could live in Manila and not have a problem.
My military career included aircraft mishap investigator for the USAF and structural engineer for Phantoms for the RAF. The RAF used, among other alternatives, refurbished J model F-4s that were from the U.S. Navy. Because I once looked at an F-4, I was selected to advise and work for the Brits as a structural engineer. Some of the J models had been hosed with salt water due to aircraft emergencies while in the USAF. It is simply amazing where you can find corrosion after that happens. Anyway, several years of investigating why things come apart gets you a basic understanding of it all. Like most things associated with aircraft, the field is huge so you depend on lots of people to help.
Inventor of the world's first safety vibrating Kamisori with night light. Go to http://badgerandblade.com/vb/showthread.php/299465-A-milder-Kamisori: Inventor of the Weckisori - (thanks sychodelix)