What makes you think you'll blow the device.
As far as your device is concerned, it doesn't care whether you power it from the national grid, super capacitor, battery or two wires stuck into a potato.
The ability of a power source to provide current has no bearing (or is it bareing) on a devices current demand. (OK the purists will argue that the source impedance will affect current delivery capability but that only applies if you are demanding more than the source is designed to deliver)