You can still have one cable to the wall - just a standard USB charger. If you add a battery to your pedalboard, you can treat it like a laptop, i.e. leave it plugged in most of the time so you don't have to worry about the battery, but unplug whenever you need to be mobile!
However, if you're looking to power a HX Stomp from a battery, you'd have to invest in a rather large one!