Charging from a battery

Use a switching buck regulator from an appropriate battery? Check the required current for your system, but I would guess that 50-100 mA should probably cover it.

Or perhaps a USB power bank?

As far as I can tell, that circuit should do the job of auto shutdown (with the right code), though I'm not quite sure why it's switching GND rather than Vcc. A proper circuit diagram might make things clearer...