It might help to look at the LED flashlights containing a 'shaker' device which will charge a battery (capacitor? supercapacitor?).
I'm pretty certain it consists of a coil of thin wire. A magnet travels back and forth in the center of the coil.
Alternating positive and negative pulses emerge.
A diode (or diode bridge, etc.) rectifies these into DC pulses, to charge the battery.
Mechanical motion will be well soothed for this project .I think Mr BradtheRad got the idea of the project but in my area here in Lagos LED flashlight that contain a shaker is not common but can you throw more light on how we can actualize the second option you mentioned.