Now, I was skeptical, because we're not talking actual good-quality leather shoes, here. We're talking cheap fakes. But he insisted, so I went to a shoe store (one of the nice ones) and got myself a bottle of black shoe polish.
The shoes do not look new, but they are back in the firmly professional category. And not only those shoes. I also tried them on my black tennis shoes. Again, not real leather, and this pair had places where the top layer of the vinyl had come off. With polish, you have to look very carefully to see where those places are. They no longer look like "good for nothing but yardwork," I can wear them out and around town.
I got the bottle of polish for like $9, and it will be enough to last me for years to come even polishing all my pairs of black shoes on a semi-regular basis. It will save me so much money in not having to buy new shoes.
And, best part? It's this new thing where you don't have to brush the shoes or polish them after. You just make sure the shoes are clean and dry, daub the polish on with the included applicator brush, and let them dry. That is it, that's all you have to do. The same company (tarrago) also makes clear polish, so you don't have to get a bottle for each different color shoes you own. I don't think the clear polish would cover the places where there's an actual layer of vinyl missing, but it would probably get rid of scuff marks.