I saw a tv once with a hand cranked generator built into it. It didn't seem very heavy,
so I don't know what kind of batts it had in it.
The guy said he got about equal time between cranking and being able to watch tv.
I would imagine the screen required a lot more draw than a flashlight, so the genny
from something like that would prolly quickly charge a 3.6v batt.
Of course, the last time I saw one it was about $120.
I guess it would depend on how often you thought you would need that kind of back up.
Maybe you could find the genny by itself on some kinda place like Alibaba.