We know that at least four starships on the charts are not Constitution-class ships. USS Excelsior (Excelsior-class), USS Oberth (Oberth-class), USS Constellation (Constellation-class) and USS Lantree (Miranda-class). (USS Whorfin may also be something different)
USS Potemkin is a known Constitution-class starship, and USS Kongo is likely one as well.
USS Endevour, USS Republic, USS John Muir, and USS Helin are also likely Constitutions.
In my head canon I think they are the following from Operation Retrieve. (Hi btw, first post.) Hopefully I will post a discussion soon I would like some input on.
USS Whorfin NCC-1024 Oberth-class
USS Republic NCC-1371 Constitution II-class
USS Scovill NCC-1598 Oberth-class
USS Potemkin NCC-1657 Constitution II-class
USS Helin NCC-1692 Oberth-class
USS Kongo NCC-1710 Constitution II-class
USS Lantree NCC-1837 Miranda-class
USS Emden NCC-1856 Constitution II-class
USS Endeavour NCC-1895 Constitution II-class
USS Springfield NCC-1963 Miranda-class
USS Constellation NX-1974 Constellation-class
USS Excelsior NCC-2000 Excelsior-class
USS Korolev NCC-2014 Constitution II-class
USS Challenger NCC-2032 Excelsior-class (Due to the fact Constellation is still an NX or maybe a Constitution to match the other shuttles.)
USS Ahwahnee NCC-2048 Constitution II-class
USS Eagle NCC-956 Constitution II-class
USS Oberth NCC-602 Oberth-class
USS John Muir NCC-1732 Oberth-class