While it may not be as common as 18650 or especially a AAA. A 14500 battery is as small as an AAA while retaining the same chemistry/voltages of normal lithiums you see used with a nice nano. Could be your best bet if you want small but easier to source/replace. An 18650 is your best bet on availability though, but they are huge compared to what we normally use.
AAA batteries operate at 1.5v nominal, so a nice nano would not be able to be powered by them/it would overcharge it.
🥹 love it! Now add magnets!