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There is a book "Mercy Ships: The Untold Story of Prisoner-of-War Exchanges in World War II" which covers this topic.
The two principal ships used were Swedish: Drottningholm and the Gripsholm.
These ships were also used to exchange civilian internees. The total amounts of people exchanged amounted to a few 10s of thousands. In the case of soldiers, it was mostly sick or disabled soldiers that were exchanged.