Was it correct not to shake hands with the Christian student?

The priority should have been to greet the disbelieving student to win his heart, as there is no impediment to greeting a disbeliever if he is among Muslims. The Prophet, peace and blessings be upon him, greeted a mixed group that included polytheists and Jews. Scholars have differed on the ruling of initiating a greeting to a disbeliever and returning his greeting.