In pure onscreen terms, the E-C doesn't appear outside the parallel timeline. If uniforms can change back and forth, ship designs might as well. OTOH, again in pure onscreen terms, the design we see is never identified as Ambassador
class in our reality; this terminology only ever refers to the unseen Horatio
It would be pretty darn difficult to argue that the Sternbach-style E-C is the child of a warlike timeline, though, when the "peacelike" regular timeline sports so many ships of that design (and none of Probert's intended one).
As for the "intent" of the wall relief, we have two ships there that don't match the looks of known Enterprises
already. Even the aircraft carrier is suspect, as in ST4 it was seen that CVN-65 sported a distinctively slimmer island farther forward.
Then again, the "cube island aft" look for the ship is also multiply redundant canon, from other wall artwork (namely, Archer's Ready Room), so we might be speaking of an extensive refit there. Which makes sense, as the cubical island is a relic of 1960s radar technology, and may have been dispensed with in the 1980s. Perhaps the ship is generally remembered in her 1970s guise for her central role in the Icelandic Torpedo Crisis?
The other fairly obvious option is that the ships on that wall are all proud carriers of the name Galaxy
. (Sure, a fairly odd name for a sailing ship, considering the modernity of the astronomical usage of that term, but by no means impossible.) Or then Picard asked for a wall of ships named Stargazer
, perhaps a more likely choice for a sailing frigate (and if an aircraft carrier can be named Shangri-La
, then nothing is out of bounds there!).