I'm willing to say that with the Klingon Empire consisting of so many people and stretching across many planets, the odds of the average guy picking out Worf was pretty much zero. It's not like he's got a reality show, you know? They do make mention of him steering clear of Gowron, if I recall, and that was probably enough. Even he probably wouldn't recognize him outside of his "child's uniform."
I always thought it was silly that they sent O'Brien on the mission, especially in make-up that made him look like Kletus the Slack-Jawed Klingon, when it would have made much more sense to send Jadzia, who already knows a ton about Klingon culture and could have done the simple job of setting up the laser-beam-thingies just as well as O'Brien could.
"Kletus the Slack-Jawed Klingon,"
As for Jadzia in Klingon make-up... that would have made more sense and would have been totally awesome to see, but I doubt Worf would have been able to handle that. They would have never left the metal slab in his quarters.
(and yes, I know we are still a few episodes away from them being together at this point, but seeing her as a Klingon woman would have definitely sped things up.)