Speaking as one who started riding in the days when natural leather chamois was all there was... don't. Really. I didn't think they were still available, and there's a reason for that.

They take a lot of care. They're easily ruined. And even with the best of care, they will quickly stretch out and/or harden to the consistency of sandpaper.

It's true that shorts with a good thin chamois aren't that easy find. But like I said, I didn't even know that natural leather chamois were still available, so they're obviously even harder to find. Get synthetic.