Using portable USB charger with Electronic Cigarette?

My electronic cigarette has a USB charger for using with a computers USB port. It also has a box that can store charge for charging the e-cigarette on the move. My question is could I use a standard portable USB charger (e.g. the PowerMonkey Explorer or something like this) for charging my e-cigarette using it's own usb adapter? I think this would be better since maybe a generic 'on the move' charger can store more power than the box charger that came with the e-cigarette? But I'm wondering if this would work and not cause damage by overcharging?

===========
electronic cigarette