Actually, has there ever been an exact and accurate portrayal of a historic setting in the holodeck? Our protagonists wouldn't be able to tell right from wrong unless it was a contemporary item.
I think it stands to reason that the only available artifact from which to create this holodeck illusion was a Constitution Class starship, in particular the one from the fleet museum Picard mentioned, but not
the TOS Enterprise
@ Mario de Monti & QuinnTV
You got it right. It was the special "Relics" issue (# 90) of the fan club magazine. From his own fan made bridge, Steve Horch had saved the chair, the helm/nav console and two chairs. Everything else was reconstructed based on original pictures. They even invited Bob Justman to check it out and he had to tell them, that they got the floor carpet wrong - the original one was grey but not brown.