It's possible to "play the game" without killing. It's not possible to play through all the quest lines without doing so.
I have a character names Paxelle, who is a no-kill mage. She has managed to finish all the mages guild recommendations, plus a couple of additional MQ quests (she has a mage's staff.) She is also the Hero of Kvatch (some hero; the Kvatch Guard did most of the work, and as for Oblivion Gates, all you have to do is a combination of sneaking and sprinting.) The hardest thing is getting items that you'd normally have to kill for, like keys -- as it happens, you can loot people who are paralyzed, without hurting them. Invisibility helps a lot.
But most quest lines have some point at which the player-character is obligated to either kill something or abandon the quest. That's just the way the game is designed. And even if one can find a way around that requirement, the complications get so silly and unrewarding that it's just not worth the trouble.
I still load Paxelle and play from time to time, but we have no illusions that she's going to complete a lot more quests.

My own belief is that coercing anybody or anything to kill a Troll or Wolf for you is philosophically no different than killing the Troll or Wolf yourself. If a crime boss orders his enforcers to murder a rival crime boss, he is considered to have had a hand in that murder even if he didn't physically pull the trigger.
I agree with you. In most instances, Paxelle's practice has been to take the matter to the police. That is, she runs to the guards when somebody attacks her, and lets them handle the matter. The contortions of "non-killing" that were necessary to get through the Skingrad Recommendation were so bogus that it eventually soured me on the concept, and it became a chore to get through that recommenation. It was one of those challenges that you take, realizing that you're not really role-playing, just to explore the limits of the possible.