I chose capacitors because of all the problems with overcharging batteries (and I'm no expert), so I don't want things to explode..
overcharging a cap will make it explode just as quick
What about this?http://hackaday.com/2005/12/06/supercap-9v-battery/I understand these wouldnt work too long such as this...http://www.popsci.com.au/diy/article/2008-02/make-instant-charge-screwdriverBut that seems to be under a bit of load, would an ardiuno and a few other not so heavy use components (umm like say switches, leds, maybe sd card reader?) last a bit longer? If you had say an hour or two of use for example for a 60 second recharge that would be pretty cool depending on the project you made.