I mean, it's an interesting idea if anyone wanted to do a book on it. My personal effort to list the Constitution class ships as of Kirk's statement in "Tomorrow Is Yesterday" is as follows. Of this, I would say we can assume the USS Constitution was not race specific, just for the fact it was the first ship. We also assume the ships we saw on screen as not being crewed by Tellarites, or otherwise have indications of that from canon reference such as Kirk being stationed there or a human captain. This eliminates the Constellation, Defiant, Enterprise, Excalibur, Exeter, Farragut, Intrepid, Lexington and Republic. From Star Trek IV, the Yorktown also seems like a candidate for elimination. From non-canon sources that are the flavor of the moment, we can eliminate the Eagle and Endeavour. That leaves us with the Hood, Kongo, Potemkin and Valiant. Of course, this is all based on my memory and supposition. And there is the possibility that there was another ship not on the list which was never mentioned, but was lost prior to 2267.
USS Constitution (NCC-1700)
USS Constellation (NCC-1017) (Destroyed 2267)
USS Defiant (NCC-1764) (Lost 2268)
USS Eagle (NCC-956)
USS Enterprise (NCC-1701)
USS Endeavour (NCC-1895)
USS Excalibur (NCC-1664)
USS Exeter (NCC-1672)
USS Farragut (NCC-1647)
USS Hood (NCC-1703)
USS Intrepid (NCC-1631) (Destroyed 2268)
USS Kongo (NCC-1710)
USS Lexington (NCC-1709)
USS Potemkin (NCC-1657)
USS Republic (NCC-1371)
USS Valiant (NCC-1709) (Destroyed prior to 2267)
USS Yorktown (NCC-1704)