I think you might struggle to be honest, anything that has to 'create' additional signal (delay, reverb, looper) rather than modify a signal that is already there (od, mods etc) or amplify in a crude manner (fuzz, distortion) just require quite a bit of current, regardless of whether they're digital or not. But my guess would be analogue all the way! I seem to remember the Way Huge Aqua Puss RI being low...
I've used the Carbon Copy for this. With a fresh battery you'd think it'd be good for about 15 hours. I found that the sound quality deteriorates after less than 10 hours.
Above selections are great. I have experience building battery boards, even had a custom power supply built that ran off a RC car battery (tons of capacity). So I understand shopping with mA in mind Carbon Copy would get my vote over the VT, but not by a huge margin. The Violetta is tiny and has its own battery and sounds good. Really any analog delay would fit the bill nicely!