You can't.
If you go by UESPI wiki's quest stages, you can see that there's no stage where a diplomatic solution was accomplished. Not to mention that the Imperial Order item that you can only get from the console appears to be something that they were working on but didn't finish (just read the letter to see what I mean). Also, there is no "Imperial Legion Armor" in the game, no idea how that rumor about wearing imperial armor to trick the guard started.
It seems to me that they originally were going to have a diplomatic route in the quest, but either it was removed at the last second, or it was never finished and the quest as it currently stands was submitted anyway.
To me, that is really unfortunate and I wish Bethesda would make an official remark about this quest and if they will ever consider adding the route in a future patch/DLC. As it stands now, I refuse to finish this quest until Bethesda makes it known that they will never fix the quest (and if they do fix the quest, I'll wait until they do before finishing it).
