No batteries power method (induction, motion, heat etc)
Some deep-space vehicles use radio-active thermal radiation + thermo-couples to produce electricity.  Obviously, you can't use a radio-active source, but you might want to research how much energy could be generated using body heat + ambient heat for your system.  If there is sufficient energy, then you may be able to power your tiny system
Another possibility is harvesting kinetic energy generated by walking--however, that would require more hardware than simply using a high-energy cell in your system--so unless weight &amp; cost aren't majors factors, then that idea probably won't be useful.  Nevertheless, check this out.  Here is another reference that may be useful to you.


Note:  I imagine your best choice would probably be a rechargeable li-ion cell though, with respect to overall cost &amp; weight factors.