YouTuber Kyle Hinckley (under the YouTube profile The Weirdist) has managed to complete Fallout 4's main quest line on Survival difficulty without killing anyone, and recorded it all for his YouTube channel. Overall there are 37 episodes, each about half an hour long (large chunks were cut out as to not take up too much time, such as the encounter with Kellogg which took some retries). However though he didn't kill anyone, he may have had to use some tactics to get anyone opposing him killed for him, which required high charisma that allowed for him to convince people to kill others, which doesn't count towards his overall kill count.
In an interview with Kotaku Hinckley mentioned that he was "disappointed with the lack of diplomatic solutions" within the game compared to previous entries within the series, yet he still managed to push through even after Fallout 4 director Todd Howard said "I can't tell you that you can play the whole game without violence - that's not necessarily a goal of ours". Hinckley commented on this, saying that "The thing about Todd Howard is, even he doesn't know what his games are capable of".
You can start watching the 37-episode playthrough on Hinckley's channel here and watch how he uses various tricks to outsmart the game without breaking it.