Years ago I recall watching my home town barber shave my Great Uncle. Guy, the barber (also the mayor), used a piece of rectangular tissue paper (actually a bit more robust) placed on my Great Uncle's right shoulder to wipe the blade.
I've taken to the same thing, except I just use a towel. The only water that touches the blade is after the shave when I rinse only the blade with very hot water. I give the blade a sharp shake, edge down, then wipe with a dry part of the towel. I leave the razor open until I'm dressed (and have my glasses on), then give it an inspection. Normally I pinch the blade between the towel at least two more times, fold up the razor and put her up. Using this method, there is no water that gets on the shank or between the scales. When I first started using a straight I would rinse lather off as with a DE, and everything was wet. Then I remembered Guy's method.
If going into storage for a bit, some baby oil does fine.