Always keep water/lather out of the blade pivot area. The pivot area is hard to wipe dry and is a prime location for water stains and rust to begin. The only time I had a stain/rust issue beginning was when I let water get in the pivot area of a carbon steel razor. Preventing stains and rust is a lot easier than trying to remove these blemishes.
After shaving, I rinse the razor's blade below the shank/pivot in hot running tap water and wipe dry. The heat helps dry the razor. Keep the blade tilted down to prevent water from running into the pivot area.
I then strop the dried razor and wipe the blade and between the scales with a small rag slightly damp with camellia oil. The oil damp rag is stored between uses in a small plastic former pill container always ready for use that I keep next to my strops. The wipe rag can also be used to wipe carbon steel kitchen knives. The rag is only slightly damp with oil, but leaves a thin barely visible film on the wiped blades and does not leave fingers wet with oil.
Any good steel protecting oil such as a gun oil would work, but camellia or mineral oil are often used because they are eatable oils and any residues that may remain on a blade wiped clean of oil should not adversely affect ones face. Camellia oil is sold by tool and knife vendors and has been used on Japanese swords.
I wipe my straight razor blades and scales once in a while with Renaissance Wax, but a silicon wipe for firearms preservation would also be good. Wipe preservatives off the blade immediately before restropping done before the next razor use. Storing razors in humid heavily used bathrooms may be risky for rust.
Always wiping your razor with an oily rag after use or touching metal as a ritual (as is done with firearms) will ensure that you will never pickup your razor that has not been used for a while and wonder where the rust came from. For me, looking at an unnecessary cosmetic blemish caused by neglect before each shave, especially one caused by me, is an unpleasant reminder that detracts from each shaving experience. I expect to see normal wear and tear on a well used razor.
HTH