This is what I found after extensive searching:

Reparata and the Delrons had indeed a song in 1968 called "Captain of your ship". It was written by Kenny Young (same guy from "Under the boardwalk) and Ben Yardley. The latter also uses the pseudonym "Estelle Levitt".

Concerning the cover I found a lot less. Your own source for example says it's not on the "Very best" but on an obscure album "Only you can". Found nothing else right now.

I guess that if Fox have a cover called "Captain of you Ship" it's very likely a cover of Reparata, as one of the band members of Fox is Kenny Young himself. However, the question remains when this song was released, and on what album.

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