The v p guy can’t be selected after the electoral college votes. He can be elected by the electoral college when it votes, however. The most interesting legal issue would be if the electoral college elects someone president and then said person passes away before being sworn into office.
IIRC, I believe that would be the simplest issue to solve. If the President-elect dies before the inauguration, the Vice President elect would be sworn in as VP at 1200 on Inauguration day, then immediately succeed the deceased President elect, and be sworn in as President.
He/She would then nominate a VP and the Senate would have to confirm them in office.