An Adafruit Powerboost1000 with a TP4056 lipo charger (with protection) should be ample if you use the standard brightness of 10.
Reference images are in the images folder. Arduino IDE setup instructions are in the Software folder. All the parts you require including the Gerbers required to have the PCBs manufactured are above, start by reading the assembly pdf. I wish you luck and I'd love to see it if you make one, catch me on Twitter(@HiboTronix) and/or tag it with #Discoball : )
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