You could do this with any stone. But I would pick a trans or black ark and a cheap diamond card to raise slurry on one side (and I'd never touch the other side with anything other than a cloth to clean it from time to time).

Actually, the only person I know who has shaved for decades does just about what you said. He strops his razor on horse leather, and in his terms, "once in a great while" he runs his razor over a black arkansas stone that he uses for woodworking, but that he's been careful to not lap so as not to lose its fineness. Same razor and same stone since the 70s.

He has a level of economy and a lack of curiosity in this are that I could never match!