When I got my first pair of bike shorts in 1983, it was pronounced chamois. They were awfully difficult to find back then. They were wool with real leather chamois. No one, in my experience, said "shammy" back then.

While I am in the US, I have alot of connections to France, including citizenship, language, and I'm a general francophile, so I probably say chamois for that reason, too. I actually saw a real chamois in the Alpes about four years ago. It's like a caribou, I guess, but it lives in the mountains and has a big fuzzy rear.