On a movre serious, hypothetically possible note:
I have some 6v batteries at a 1ah rating that could be stepped down. the ones I have are SLA, but I am sure that you could find a way to put a protection circuit on them.
(1lb)
using this solar charger on the backpack:
Replacement Batteries,SLA,AGM,GEL batteries,solar,alkaline,lithium,battery chargers
(at only 1 lb)
a 3 position switch could be used for charge/off/vaping for power flow control.
From there, a stepdown to 3.7 or 5v (or a vari-volt) and add in a protection circuit scabbed from a trustfire battery to keep it from blowing up. stripping a passthrough to extend the cord to the user, add the VV circuitry to a small box/tube/whatever container with your manual button for activation. a nice gooseneck going to the connector. add atty/cart and you are good to go.
you could always put a juice feeder in the VV control box with tubing running up the side of the gooseneck. Some split tubing or shrink tubing would make it pretty.
I am betting that if you put a charge jack instead of the solar panel you could get it to fit in a large cell phone holster or a hip-pack if you want to go throwback retro 80's style. Should keep it nice and portable.
I am not an electronics expert by any means, so it would be pointless to flame me for any mistakes, but other than the battery not being protected I dont see why this wouldn't work.