How? It would not. There was no reason to place one outing above the other (if both of you were villagers). It didn't matter which one of you was lynched first, since the next day the other would be lynched. I tried get people to lynch AOK first because he would have had the power to escape the noose the next day. It there was a risk trespoe (or AOK) would be the seer, the village would have lynched the non-seer-target first. (AOK already tried to get out of a outing in another game by telling people he was the seer himself, which worked). You telling the village that trespoe was the seer would have made sure AOK got lynched first, because noone would have risked lynching the seer.
And then we wolves would have to hunt Trespoe (now we hunted Randy), and Randy would have lived for another day, he surely would have exposed me as a wolf. I think then you would not have to argue as Brugman for that to happen. People would have believed you if Randy told then that he told me Trespoe was the wolf. That could indeed have changed everything.