Of course the choice is your father's.

The procedure may find nothing, but it could also find a regrowth. If there is nothing to find great, but if a small cancer has started again and he chose not to take the test he won't know til it may be too late for treatment to be effective.

My only suggestion would be to get the opinion of a cancer specialist. You did not make it clear whether your dad's Dr. who advised the test is his gp, or his cancer Dr..