Using Faraday Shake Generator to Power 4.5V LED Flashlight (Q5 Cree, 3xAAA)

Hello friends,
I have some led flashlights that take 3 AAA batteries. I wanted to replace this with a 4.5V rechargeable battery/capacitor And a shake generator (Faraday) in the battery compartment. 
5 Pack Ultra Bright LED Flashlight Torch 7w 300lm Adjustable Focus Zoomable Q5 Cree Tactical Light 
https://www.amazon.com/dp/B01D8DRFFI/ref=cm_sw_r_cp_apa_Tqj8BbAZB3BX4
The flashlight I only would need for 2 minutes at a time. 
Would it be possible? 

Taylor, The flashlight that you link to is only one AA battery not 3 AAA batteries so you would only need to generate 1.5V instead of 4.5V but at a much higher current. The biggest problem I see with fitting a shake generator in the battery compartment is that there is not much distance to get a good movement for the magnet through the coil. I'd be inclined to try this first with a physically longer flashlight and then experiment to shrink it down.It sounds like an interesting project. Let us know how you get on with it.
Elizabeth

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