I'm fairly sure it is/was patent leather, which was common on Footjoy golf shoes. This pair was totally lacquered over with a black coat of something, probably cheap liquid polish. They have a number stamped into the heel, like they were rentals at some club. Rather than care for them, they got shlacked a few times with something paint-like.Is the shell toe and facings shell you think?
I remember removing it taking a lot of effort, bit not exactly how I did it. I know I used hot water and possibly Dawn, followed by some solvent I had. Whatever chemical I used deglazed any patent finish along with the lacquer. Alternatively, It could be something synthetic like Corfam. I see now how it looks like it could be old shell, but during all the earlier work I did, this was not the case.
They aren't an easy restore, but it's doable. In my opinion, they should be resoled, which is why I'm out. I have a list of other work I'd like done on my shoes, and these would fall near the bottom because I'm already past the point of diminishing returns.