I'm worried about the long term stickiness of the LEDs/Timers/ICs. If I was to buy this I'd probably stick foil to the adhesive bottom of the components so they can be rested on top of the copper tape. That or put a few pins on the +/- areas. That way you can tape the copper to cardboard instead of paper and then punch the components through the tape.
It's the current, not the voltage.
Video for you: http://www.youtube.com/watch?v=MWuJokR_mI8
It's probably not _impossible_ to start a fire with a pair of CR2032s, but you're going to have to set it up that way on purpose – the chance of "accidentally" creating enough heat to set non-intensionally-incendiary materials alight is low enough to be ignored.
(Note, I carry a pair of these cells around in my pocket - an LED light attached to my keyring. These cheapo lights rely on the internal resistance in the battery to current limit the LED, with a white LED across a pair of cells, the battery's own resistance is enough to keep the current down under the "let the smoke out" limit of the LED - it might be more than 20mA, but it can't be heaps more.)
Then you're in trouble/on fire.