Why a carrier F-104 would require a near-total redesign

How bad an idea is a navalized F-104 arriving on a US carrier in the North Atlantic through time-travel shenanigans?

It depends on the carrier, but strengthening the F-104 for deck landings would add substantial weight and leave serious questions about operating it again.

The time-travel premise sends a navalized F-104 to a US carrier, making the carrier's identity and date essential. Ranger is considered a disastrous match, while a later carrier able to operate Phantoms could take the aircraft's weight. The F-104's spindly landing gear remains a separate problem. Strengthening the airframe and undercarriage would add weight, with an empty weight of roughly 15,000 to 16,000 pounds suggested for the modified aircraft. Even after a landing, getting it off the deck again would remain doubtful. The resulting aircraft would require such extensive alteration that it would be substantially different from the original Starfighter.