You are correct that D. Let both sides, for the first time, formulate serious and precise proposals for the inspection and control of arms... also demonstrates Kennedy's concern about nuclear weapons, as it emphasizes the need for serious proposals regarding arms control and inspection, which is crucial in addressing the risks associated with nuclear arms.
While C highlights the alarm surrounding the spread of nuclear weapons, D more specifically suggests a proactive approach to managing and controlling them. So, D can indeed be seen as a stronger support for the inference that Kennedy was concerned about the use of nuclear weapons. Thank you for pointing that out.