I won't say it isn't possible, but to the best of my knowledge, any hollow grinding needs to be done with a wheel. The shape of the hollow is defined by the size of the wheel used. Since low speed is not a problem, wheels can be made from a lot of materials that you might not think of, like MDF, and and abrasive applied. I've read that back at the height of straight razor production, the grind wheels (which could be a couple feet in diameter) were often made of wood planking, with the grinding surface being a layer of lead with the abrasive embedded in that. Talk about dangerous for the workman!
Unfortunately there are not many here who make razors specifically, and I'm not sure how active any of the straight razor forums are anymore, you might have to search archives rather than ask for help with the razor. There is a quite a difference between razors and knives, so very few people work with both.