To extend the life of a cartridge razor blade, should the blade be stored in oil or alcohol?
Most blades are dulled by either the edge folding over itself, or small amounts of rust forming. To stop the first problem, you can strop the blade, but that's not really chemistry. For the second one, anything that stops oxygen and water from reaching the blade will stop it from rusting.
Silica gel does absorb moisture,so that would prevent rust from forming, but this would be temporary. You would have to replace it, and even then it might not stop 100% of moisture from reaching the blade.
Oil might prevent water and oxygen from reaching your blade, but it would make it... oily. If you are okay with that then it would probably be a fine solution.
Alcohol would prevent water from reaching the blade pretty well, as well as disinfect it. This might be the best solution to extend your blade's life. Just make sure you use medical grade alcohol.
Finally, blow drying or towel drying your blade after every use will help a lot as well.