if you get a cell phone battery pack, the battery inside is 3.7vols.
you can connect a booster to pump that up to 5v, tied directly to the battery.
as for speed of charging, I get paid on Fridays and by Wednesday, I am low, the money goes really fast.
so, by fast, if you mean about 4 days, you should be fine with any charger.
External USB batteries will generally cut off USB power output supply after a couple of seconds, when the connected USB device is drawing too little current.
The intended use for such devices is to act as a mobile USB charger for smartphones.
A current sonsumption of 80mA should be enough to keep thexternal USB battery running until its battery is empty.
A typical "UNO board" has a current draw of about 55 mA only, so you's perhaps add some power consuming components like two or three brightly glowing 20mA LEDs to your circuit, if you are planning to run an UNO from a USB powerbank attery for some time in mobile mode.