The derivation from
Peter seems to be the correct one. The "Latin for traveler" comes from confusing the name with
Peregrine, which does have that origin.
Of course, Tolkien has confused this issue because the full name of his hobbit character Perrin in
Lord of the Rings is
Peregrine Took. So one could say that in modern times Perrin has been used in literary sources as a pet form of
Peregrine, but its origin as a male name in medieval English was as a pet form of
Peter.