I could see either the Earth Government, Starfleet and the Vulcan government (Post Kir'Shara) deciding to hide what the Romulans look like ...
This would work and make sense. It could even be incorporated into a episode when the hero ship encounters a intact body and are sworn to secrecy by Starfleet Command, or they capture/rescue a living Romulan and (ominously) have him taken off their hands by government officials.
Part of the take no prisoners policy could have been to conceal the Vulcan Romulan connection.
Hardly 'this would work'.
It involves actually assuming no one of the thousands of the soldiers/civilians who saw living or dead romulans/remans or performed a DNA test on them decided to speak, instead willingly participating in an orwellian conspiracy - for decades.
The 'remans were used as ground forces' hand-waving doesn't work, either - a DNA test on a dead soldier will easily reveal he's, essentially, a race of vulcans.
Either ignore the 'Balance of terror's ~'we never saw romulans' one-liner;
Or state there were no ground battles in the romulan war - the romulans exterminating from orbit every colony/world they captured via nuclear holcaust. This would fit with what Sisko said about the war, too.