The Navy's solution was a start unit that could be carried as a store shaped like a World War II external fuel tank, shown here on an early production Douglas F4D Skyray:
It incorporated a amall AiResearch jet engine, designed as an APU (Auxiliary Power Unit), to provide the air. Panels were opened or removed to expose the APU inlet and exhaust, the attachment of the air hose, and the control panel.
Also stowed within the cart were the hose, wheels, and a handle to pull it along like child's wagon.
The pod was often present at airshows at civil airports, carried there and back on a standard external stores pylon.
It remained useful to the Blue Angels up through the retirement of their A-4s powered by the J52 with an impingement starter:
Also see http://a4skyhawk.org/2c/a4start.htm