L&O: Criminal Intent is pretty low on the guns & knuckles scale.
Concur that Barney Miller is probably the all-time winner. I remember a scene where Fish was being taken to the hospital and somehow convinced the ambulance crew to let him go.
“The gun helped,” he explained to Barney.
Dammit, I knew something sounded weird when I typed his name. I’ve only watched every episode since the debut. 
The OP asked for cop shows where the main characters rarely shoot or punch - Patrick Jane qualifies for that even thought he isn’t a cop.
I remember an episode where Friday shot a guy trying to break into a coin machine at a laundromat. The guy fired, Joe fired back, and got in hot water when the shooting team couldn’t immediately find the bullet the bad guy supposedly fired (they eventually did).
It wasn’t every episode, but they did have use their guns in the line of duty. One early episode has Reed shoot a man, then have the investigating team interview him afterward. Malloy cautions him, “Don’t let 'em rattle you. This is routine.”
Not onscreen, but there is a first-season episode where Chano (Gregory Sierra) is forced to shoot a young man in self-defense. The episode mainly focuses on his (non)reaction until he’s alone in his apartment (this was early Barney Miller that actually moved off the squadroom set) and he breaks down in tears.
I think the all-time champion is Columbo. As stated upthread, he never seemed to even carry a gun, and on at least one occasion bluffed the suspect/murderer who seemed about to shoot him by saying the (nonexistent) patrolman backing him up outside would just arrest or shoot her. Classy.
That’s got to be the winner. Columbo hated guns and only fired one once in the entire series, as far as I remeber – and that was into a box of sand as an experiment to see what the sound effect would be.
Which was a bit of a retcon, as in some earlier episodes he indeed had a gun, though I don’t know if he actually fired it (WAG probably not).
Barney had a gun, but kept the bullet (singular) in his pocket.
Likewise Midsomer Murders, 10+ seasons and I don’t recall a shot fired by the guys at the CID. They don’t even carry weapons. Barnaby does wait unitl every suspect is murdered before he makes an arrest though, so there is still plenty of violence.
The British series Dixon of Dock Green was another non-violent police series. It ran for twenty-one years (1955-1976) and I believe only one person was ever killed in the series.
Though to be fair, the Law & Order show replaced officer involved shootings with courthouse step shootings.
I remember that episode! Reed calls his wife to tell her why he was going to be late, and tells her, “I killed a man tonight”, breaking up as he did so.
There was an episode where a gun-toting Andy confronted a would-be bank robber who had been pretending to be a director making a movie, trying to find weaknesses by asking all kinds of questions about how small town officers worked. His reaction to getting caught was “I thought you never carried a gun.”
Andy’s reply was that he didn’t say he never carried a gun, just that he usually didn’t. He certainly wasn’t dumb enough to go after a bank robber unarmed.
Nearly every time they were going after a real criminal he would grab a sidearm or a rifle from the armory before leaving the courthouse. He also occasionally gave Barney a handful of bullets and told him to load up.
The bullet pushed the shelf up and went into the wall behind it. Joe noticed the line on the bottom of the shelf. That’s one of those odd things that’s always stuck with me.
Not at all fictitious, although since the show started there have been some changes and the name is now just BI. Though the job they do on the show bears as much resemblance to what the [C]BI does as about any other show of its type.
Forgot about those, but all-in-all, firing guns, or even drawing them, was very unusual on the show.
Actually, Prez fires twice in the series while on duty:
The crucial shot in Season 3, and also the (accidental) shot into the wall of the basement office at the very beginning of Season 1.
American Police show: Halt, or I will shoot
BLAM
BLAM
BLAM
BLAM
British Police show: Halt, or I will yell Halt again!
(yeah it’s a cheap joke but somebody had to do it)
Batman never used a gun 
Los misterios de Laura; they do have guns (being cops and whatnot), but in most episodes the only violence being commited is what led to having a corpse in the first place. Los hombres de Paco (named after los hombres de Harrelson, SWAT in the original) had the occasional shot. Laura is currently running in RTVE (Spanish public television), Paco’s was Antena 3 (a private chain, also Spanish).
Laura is a fortyish separated woman with kids, an ex who’s more infantile than the kids, a widowed mother who’s always in search of new husbands for both of them, and a family which does things such as murder each other in the middle of a wedding. Oh, she also happens to be a homicide inspector.
Paco was the comisario (captain) of a precinct in one of those parts of Madrid which can have super-posh flats with 6 bedrooms and 4m ceilings in one block, half-run-down tiny ancient poor folk’s apartments just across the street.
The cops may be non-violent but I have learned from those shows that the English countryside is awash in blood.
And he fired blindly into the towers after he knocked that kids eye out and bottles started raining down.
I think he may have thrown a few punches though.
early cop shows might have had this, it may have been a carry over from radio where you had to always have meaningful sound (long chases didn’t work well). though movies from the same period as radio did the same as i recall.