Good to know, I'll see if I can find a 1A system.You would only lose half the power using a linear regulator. A switching regulator can be 90+% efficient.
If you want small, a lithium battery is the way to go. You can get solar charging / lithium battery products already built that output the 5V you need. They call them solar phone chargers. But the beware, most are not sufficient for to run a 1A load continuously.
Bob