Figure skaters often use a material that looks like leather or vinyl but is neither. It is soft and supple--of course it would have to be to skate in it.

You might check out sites or specialty stores that sell fabric for this purpose

If you do a search for "fake alligator fabric", you will find quite a lot of options.

Here's one -- purchase link is below:

Here is a link that might be useful: fake alligator

That photo looks like either real snakeskin (the belly skin), or pleated kidskin to me. If that's out of the question, many fabric stores have novelty faux leathers for sewing....