As another mentioned, use a relay to isolate the higher amperage circuit from the lower amperage circuit. A bigger fuse is begging for a fire. Although, once you create the new circuit, you need to put the bigger fuse in that circuit. Otherwise it would be an isolated and unprotected circuit.

Get a cheap relay, some leds, and a power supply to play around with. Cheapest power suppliee are the ones sold for rc car racing chargers. Protek. Mine can do 20 amps.