For what it's worth, here's what I use for a razor stand:
My wife found this one in an antique store, but you can find them brand new still, on Amazon. I spread the arms apart a little, so I wouldn't scratch the razor handles. As it is, it will hold 16. If I were a little more industrious, I think I could flatten each arm to make them a little longer, where it would hold 24. I recently discovered that I can add a second tier, or another carousel to this using a kit, also available on Amazon. That may come in handy, as my collection is starting to spread out across the counter: