Since I've been pulling a bunch of lithium ion drill batteries out of the trash (they will be for a Hackaday article at some point...probably), I decided to use a pair of 18650 cells in an off-the-shelf battery box. This gave me 7.4 volts (and even higher when freshly charged), which would be fine to run through the Arduino's built-in regulator, but would be too much for the LEDs themselves.

So the output of the battery goes to buck converter module which is adjusted for 5 V output. One set of wires goes directly to the LEDs, while the other is goes to the Arduino.

I added a seven-segment LED volt meter to the back of pack, allowing me to check the battery level as my  daughter goes form house to house. With a little 3D printed bezel and surrounded by fake hoses, it blends in quite nicely.