Imagine if you will it's inauguration day, and everyone's up on the steps. The new VP is sworn in, and that lets the previous administration VP off the hook. Suddenly, a shot rings out, and the current administration sitting president is fatally hit.
What happens next? Does the newly sworn-in VP, being the official next-in-succession then get sworn in as President, or does the president-elect, still a civilian, get sworn in as the new president?