I want to power one particular device that feeds of 12V (5W) electricity.

However this device is intended to be highly portable and as such, I am quite tight on space, which means 12V accumulators are too big for this purpose. Also they are in fact, way too durable (and quite costly).

The power source must be rechargeable, so that I can take advantage of my charger. It is enough if it lats at least 1 hour and I cannot afford more than 10$ for it.

What would be the most cost-effective, small, disposable 12VDC power source that lasts at least 1 hour on a 5W power consumption?

As a side note, I already have x4 LG HG2, they are hi-drain (20A) and quite durable (3000mAh). Maybe I can use some boost converter to make 12V out of it. It may last 4 times less (decrease to about 6A), but that would still be very long-lasting I think.