There are two matters in the this question.
1. The prophecy/statement
The prophecy itself is (probably deliberately) vague. For example, "stretching out the hands" may refer to preparing a person for a flogging as was the case with Paul in Acts 22:25 -
But as they stretched him out to strap him down, Paul said to the
centurion standing there, “Is it lawful for you to flog a Roman
citizen without a trial?”
Many people were flogged to death and thus, Jesus' statement could possibly refer to a death other than crucifixion.
2. Peter's Death
The actual historical material recording Peter's mode of death is also vague. We have no reliable historical record of how Peter died. The closest we get is 1 Clement 5:4 which reads:
Peter, through unjust envy, endured not one or two but many labours,
and at last, having delivered his testimony, departed unto the place
of glory due to him.
We do not even have reliable information that Peter died in Rome. (However, we do NOT have data that says he did NOT die in Rome either.) The source of the tradition that Peter died in Rome by crucifixion is found in the pseudepigraphal work, "The Acts of Peter" written about 100 years after Peter's death. In the Acts of Peter- XXXV we have -
And as he went forth of the city, he saw the Lord entering into Rome.
And when he saw him, he said: Lord, whither goest thou thus (or here)?
And the Lord said unto him: I go into Rome to be crucified. And Peter
said unto him: Lord, art thou (being) crucified again? He said unto
him: Yea, Peter, I am (being) crucified again. And Peter came to
himself: and having beheld the Lord ascending up into heaven, he
returned to Rome, rejoicing, and glorifying the Lord, for that he
said: I am being crucified: the which was about to befall Peter.
Tertullian (155-240) also alludes to Peter's death in his Prescription Against Heretics that Peter endured a death like the Lord's.
Origen (184–253) in his Commentary on the Book of Genesis III, quoted by Eusebius of Caesaria in his Ecclesiastical History (III, 1), said: "Peter was crucified at Rome with his head downwards, as he himself had desired to suffer."
This is not to suggest that Peter did NOT die by inverted crucifixion, only that the data is scant and less than solid.
The prophecy about Peter's death in John 21:19 is similar is style to an eastern oracle's prophecy and capable of a range of outcomes. This is almost certainly deliberate so that because the Lord often does not want us to know the future too accurately. As Sir Isaac Newton is supposed to have said - "God gave men prophecy, not to make them prophets, but to strengthen their faith when it was fulfilled."