I suppose will is very slightly more accurate, but I would say that either word is correct in everyday usage. The word 'will' connotes a more definite occurrence; if we say "that will happen", we are indicating that there is no doubt about it, where when we say "that may happen", we are specifically saying it may or it may not happen. In your sentence, there isn't any certainty about whether the passport will be handy, though there are situations where it will be required (that you may not foresee) and others where it is merely convenient.
But either word is correct in the sentence, and there is no real difference in their meaning here.
Best Answer
They are both grammatical and reasonably idiomatic, and have very different meanings.
means "It is possible that he will not have to go".
(which is probably less common) means something like "It is possible that he will find that he must not go."