Portapow usb charger is what I use
HERE along with the retractable cable
HERE
And will only cost you a tenner.
+1. Any USB cable with the right connector will work. I went for the coiled cable, the first of those I had I got with the retractable one. Some cables might make the Garmin think it's attached to a computer (at least it can with a 705). Spare cables are always handy, anyway. What works best in my experience for a long run is to plug the booster in at the beginning- that way a device that has enough power to actually keep the Edge battery charged (as well as powering the device) will do so. If not, you should still have enough juice in the setup for it not to go flat on you. The 2xAA Portapow can recharge the 705 under lower usage (not using the backlight much, and so on), but not in more demanding situations. I've had both- one run I did to Wantage, I powered the Garmin down for my lunch break and it was fully charged. On an audax a few weeks back, using full turn-by-turn routing, and flicking back and forth between menu screens a lot, the internal battery was drained at the end, but there was still power in the AAs and it lasted till I got home.
Battery life sounds very low there- hopefully the replacement will sort it. Garmin quote 15 hours battery life for the 705, and I've got that, or near it, a few times.