ORIGINAL: John Sohm

Try a place like Lowe's or Home Depot and check their hole saws. Look for the Remington brand. I'm not sure how small they make them but it has either a carbide cutting edge or industrial diamond (Rem-Grit or some such thing). It's pretty robust stuff. I just don't know if they make them that small. Also if you're looking online, you can find diamond edged bandsaw blades too for cutting that stuff. I've cut the thin stuff (up to .015" to .020") with kitchen shears and then just finished off the edges but I know the 1/16" is way too thick for the shears.