This is an interesting topic.
I've never actually run a game where the players have agreed to play a low violence, moral game, but I have noticed some patterns that might make it more viable.
First, when the players/PCs know that any type of combat will be deadly, they tend to avoid combat and try to find other ways to solve problems. This is the entire impetus for games like Call of Cthulhu, in which, if you actually ever encounter a creature in that game, you need to run and try to escape or you are dead meat. In my D&D games, if I slap the PCs down big time in the beginning of the campaign and most of the time they get into a fight, they start playing more cautiously.
Also, as mentioned by [MENTION=6787650]Hemlock[/MENTION], using objectives that require other skills helps a lot too. Why kill when you can sneak, talk, disguise, cause diversions, use tricks, etc. If the objective is to gather information, explore, find missing items, retrieve items, broker deals with rivals or allies, then fighting becomes a last resort. In a campaign like that, I'd be tempted to throw out inspiration and advantage for lots of actions that the players decide to use if it bypasses combat.
Another way to make combat less attractive, especially in civilized areas, is to populate the area with peacekeeping forces that have real power. I remember when I first played the video game, Fallout. (Yes..this dates me). At a number of points, if the PC killed, a swarm of others would mob him and kill him. Pretty soon I realized that sometimes killing was not the answer.
I bet you could use a chit system like dark side points in Star Wars that would scare players into avoiding really unlawful or wholesale killing. I imagine you could tell them that each time they kill for no reason, or when killing can be avoided, they will attain a "stain". (like negative reputation). When they get to 3 "stain" (or whatever you decide), they will suffer (perhaps losing their souls, or gains disadvantage on charisma checks when interacting within lawful society, or some other punishment that would make it interesting). Of course, this type of game, should be agreed upon by all players because it sets up a number of limitations. You could even have the Gods they worship speak with them or take away some powers as they progress with more and more "stain."