I have a few winding (crank) lights. They will retain their charge for many many months. Even if not, you will only need to wind them up for half a minute and you will have light. No batteries needed. Cost very little. Most with 3 to 5 LEDs thus providing sufficient brightness in emergencies.
Then there are cheaper Chinese Proton copies. They are everywhere in the house and attached to many zippers in clothes.
Except for Freeplay, those crank lights use rechargeable lithium ion coin cell batteries. So yes, batteries are needed. Problem with these is that they can overdischarge or be overcharged, and there is no protection from either. If either happens, the light will never hold a charge again, and there is nothing you can do about it. So, if you leave one sitting in an emergency box for 5 years, chances are high that it has over discharged, and will refuse to hold a charge for more than a few seconds when you really need it.
I also have about 20 of the Fauxton's sitting everywhere, and hand them out like candy to friends and family.
If you like the Nite-Ize modded MiniMags, why not just drop some Energizer lithium cells in those for your emergency lights? I use lithium powered MiniMags with LED drop-ins for emergency lights in all four of our cars. Will hold their charge for at least 6-8 years, and be very resistant to heat and cold. The Energizer lithium AA batteries are available at Walmart for around $2 each.Pretty much something about the size of a mini-mag but LED.
Something to use in the car or in the house in case of a power outage.
I have a couple of Streamlight Tasklights, a bunch of nite-ize modded mini-mags,and a Gerber Cornea.
Such as the Petzl e+lite. It uses two CR2032 lithium coin cells which will run it 40 hours easy with good light and another 60+ with dim light. Has a red led and three white leds, super light weight, can be clipped on to things, used as a headlamp or hung on anything else and can be pivoted to just about any position. You can easily tape extra batteries to it or throw more in it's carrying case. I don't know of any other emergency light that is more versatile for it's size and weight than the e+lite.A headlamp with lithium batteries.