i examined the film reconstruction closely using youtube. the posted footage i watched was "reconstruction of windjammer" and at time mark 14:18/15:01 it shows clearly the submarine in the movie closing shots. the hull number shows as 344 (USS COBBLER). The destroyer appears to be dd-758 (USS STRONG).
As I understand it, they met a task force for the filming, I am not sure of all the ships and boats present. But I heard from a sailor who was aboard during the filming, and here is a picture. Also, some underwater shots were (re)done in an underwater studio.