In the badge from the article they're using 18650s, so AA batteries would actually have slimmed it down by 3.5mm.

Lower voltage, of course.

OK, but my point is more general than reproducing the badge from the article. I was rather pointing out the lack of easily-purchasable NiMH (or other "rechargeable safe(r) chemistries") batteries that could serve as a replacement for a very flat coin cell. For instance, CR2032 (3.2 mm tall), CR2025 (2.5mm tall), and CR1616 (1.6mm tall) lithiums are easily-purchasable, and it would be nice if NiMH batteries were purchasable with those heights.

The fact that NiMH is 1.2V is another thing to consider cause their heights would add stacked, though it isn't too much of an issue cause they can be placed flat side-by-side, or could use one of those ultra-low voltage MSP430s that can run off 0.9 V to 1.5 V.

Is a lithium ion button cell (LiR) big enough to pose a danger? I can't really find any tests.

Wikipedia claims several rechargeable chemistries for button cells including NiMH but most of the seem to barely exist.

Do you need more current than ML can provide?

For the type of applications I imagine, I wouldn't need more than 1mA of current...just enough to run an attiny-like microcontroller and blink a LED on occasion before going back to lowpower mode. It seems NiMH just doesn't come in those small sizes. I don't know much about ML, I'll have to look into if ML and LiR in the smallest coin size are safe enough. Actually now that I've thought about it more I might be able to just use a small supercapacitor for around an hour if I'm really careful with energy consumption.