I thought about a small container of alcohol to sit the razor in... that might work too.
My dad used to have a mug-like container by he kept his razor in - it had a domed lid with a notch in the edge to fit over the razor handle. It was originally used to soak safety razors in a product called "Razobrite". I don't know what that stuff was like; Dad always used it with about an inch of blue Barbicide.
I think the Razobrite name is still alive - there's a company in the U.K. that sells a similar product.
I'm not sure that soaking a modern multi-blade razor in alcohol or Barbicide would produce a cost savings. Older razors were all metal, no plastic to react with the cleaning solution. Perhaps the mineral oil suggestion upthread would be the way to go... until ceramic razor blades make all this academic.
I use an old coffee cup, a funnel, and mineral oil. After shaving and washing the razor, dip the razor in the oil, and rest it in the funnel where the oil can drain back into the cup.
My razor has lasted over6 months.