If you want to blame someone or something for ending the war....it was Section 31. If they hadn't diseased Odo and the Founders, we would be in Season 26.
Not if Sisko hadn't been able to persuade the Prophets to intervene in Sacrifice of Angels, that was in season 6. However, both Odo's infection and the infection of the great Link occurred back in season 4. My guess is that, had those 2700 ships gone through the wormhole (and much more back in the gamma quadrant to draw upon), the Federation (and allies) would have sufferered a quick defeat, as their largest fleets seemed to number in the few hundred ships at best.
So, the Alpha Quadrant is conquered (or at least huge inroads made) and then the Founders are getting sick, about a year later. Probably would have plunged both the Alpha and the Gamma Quadrant in utter chaos. Sounds a bit like what the Pah Wraiths wanted all along.