Kirk would have decided its necessary for the Federation's survival and gone ahead without Garak's help. He would get Spock to keep Vreenak busy while he personally planted the bomb on Vreenak's ship.
Picard would have lectured Garak. He would then bring the Enterprise into a loosing battle with the Jem'Hadar right at the Romulan-Federation border. While fighting off the Jem'Hadar, he would appeal to the Romulans on the strategic and morale impact the loss of the Enterprise would have on the Federation and the war, and appeal for the Romulans intervene.
Janeway would have lectured Garak too. She would then take Voyager to the Romulan-Federation border and stay there for however long it takes to get the Romulans to see things her way.
I'm not sure what Archer would do. I suspect he would decide that getting the Romulans' aid is not worth the effort and concentrated on winning the war without them.
Picard would have lectured Garak. He would then bring the Enterprise into a loosing battle with the Jem'Hadar right at the Romulan-Federation border. While fighting off the Jem'Hadar, he would appeal to the Romulans on the strategic and morale impact the loss of the Enterprise would have on the Federation and the war, and appeal for the Romulans intervene.
Janeway would have lectured Garak too. She would then take Voyager to the Romulan-Federation border and stay there for however long it takes to get the Romulans to see things her way.
I'm not sure what Archer would do. I suspect he would decide that getting the Romulans' aid is not worth the effort and concentrated on winning the war without them.