How can I not snap people's necks (or only snap it a little bit)?

I've done this trick on my last playthrough, smashing the wall and knocking out the person on the other side. As I expected, I got Pacifist at the end.

So, in short, no, this technique does not disqualify you for Pacifist. That said, the criteria for Pacifist are quite weird, I think the game is designed to be lenient.

What you can do (instead of wall punching) is to use a revolver with explosive bullets on the wall. It will render the person on the other side unconscious when the wall breaks, instead of killing him (2 rounds AFAIK). It made the Tracer Tong mission extremely easy (playing non-lethal).

After taking the wall breaking perk, I found myself in the situation of breaking through walls leading the lethal deaths. I noticed that the wall had a health rating, like crates do, taking a indestructible object, a barrel, I threw it against the wall multiple times until it broke, this alerted the guards but this method works without any expenditure of grenades or explosive shots from a revolver.