The real thing to trip you up is this - players like drama and tension and stakes that are at least important to their characters, if not the game-world as a whole. In dramatic, tense, important times, it is rather likely that someone is going to try to use violence, eventually.
Now, you can give yourself a setup to make violence less common, but arbitrarily removing it entirely wil feel artificial, and hobble you dramatically speaking. You don't need dungeon crawls, you don't need armies of orcs. But to say that in a tense moment nobody will even throw a punch because of a "no combat" rule is darned silly.
So, the question you need to ask yourself (and perhaps the other players) is what kind of stories you can tell that have absolutely, positively no chance of including violence, and still be interesting to them. Get the player feedback on that question, and use that as a basis for your planning.
Now, you can give yourself a setup to make violence less common, but arbitrarily removing it entirely wil feel artificial, and hobble you dramatically speaking. You don't need dungeon crawls, you don't need armies of orcs. But to say that in a tense moment nobody will even throw a punch because of a "no combat" rule is darned silly.
So, the question you need to ask yourself (and perhaps the other players) is what kind of stories you can tell that have absolutely, positively no chance of including violence, and still be interesting to them. Get the player feedback on that question, and use that as a basis for your planning.