You best bet is probably an OKR regulator at high voltage with 2x 1000mAh or better
batteries.
- OKR for reliability and efficiency.
- High voltage because it draws let current to maintain you desired wattage.
- 1000mAh or better because users typically get a full day plus out of this setup and ~1000mAh.
With 2x 2250mAh Panasonic cells you should be able to stretch 2 days or more out of a charge. More if you spend a little more for the 3100mAh Panasonic NNP cells.