There was always going to have to be a bit of brow-beating to force the FN to stop fighting, whether Zuko had been Firelord or no. The original plan that the gaang had had back in B2, if you remember was an all out invasion of the Fire Nation by the Earth Kingdom, putting a stop to them that way.
The thing that probably worked best to Zuko and Aang's advantage was that the people of the Fire Nation are very, very compliant. They have, by and large, developed a natural instinct for looking to the most powerful people around for direction. Ozai has lost his Firebending, and Azula is suffering from a mental breakdown. They are no longer the most powerful people around - now everyone's looking to Iroh, Zuko, and Aang. Ironically, it was most likely the Firelords of the past who inspired this "shut up and do as you're told" attitude in the nation.
As to the first part of your post, I really don't think that it would have been enough. Ozai's plan to burn down the Earth Kingdom was already public knowledge - I seriously doubt he made any secret of where he was going, and Azula apparently had no qualms about shouting out the plan in public when he said she couldn't come with her. Also, this isn't the first time that the FN has done something like this. 100 years before, the people of the Fire nation had no problem with Firelord Sozin wiping out the Air Nomads - why should they have any more trouble with Phoenix King Ozai obliterating the Earth Kingdom?
Did you catch the post I made a few pages back about Julius Caesar? It is one of many, many examples that can be provided that when well respected rulers feel like smashing their "honor" to pieces to make more convenient winning a battle, their subordinates are usually quite willing to simply accept whatever reasoning they care to provide.