That seems highly dubious. Think of it like this: have you ever accidentally cut yourself with a knife to any considerable depth? Did you feel the pain (and withdraw the knife) or did you by other means realise you were hurt before you actually felt anything?
I can’t see any way of cutting throug skin and thick muscle tissue into the great blood vessels of the throat without causing pain.
This is even more clear in the case of kosher slaughter where, I believe, the knife is not allowed to sink deeper in the throat of the animal than the width of the blade. Do they wield clumsy meat-cleavers to cut the throats of bulls at kosher slaughter-houses?
If you have a VERY sharp knife, or a razor blade, it really is possible to cut yourself deeply and not realize it until you notice copious blood. I’ve done it. Most people who do a lot of cooking and use very sharp knives have done it. Surgeons have managed to accidentally slice themselves with scalpels and not notice immediately, sometimes not until after the surgery is done and they take off their gloves.
That’s why for kosher slaughter the knife must be as sharp as possible. And really, it only has to go in far enough to slice open the major blood vessels of the necks after which death follows rapidly. Those blood vessels are really very deep. There’s no reason to go deeper, and by hitting bone you risk damaging/dulling the knife that must be kept razor sharp.
There are large nitrogen tanks where I work and, while out running one lunch time, the tanks were being filled from a tanker. Running past the tanks and through the nitrogen cloud that was produced while very out of breath, I passed out without knowing it. I woke up after the tanker driver had dragged me out of the way. So I a painless death by being in a Nitrogen filled room is very possible.
Your body relies on a buildup of CO2 in the lungs to trigger an urge to breathe. Inert gases make it possible to painlessly reduce O2 concentrations to dangerous levels long before CO2 builds up and makes you gasp for breath.
There are countless YouTube videos of people sucking the helium out of balloons and - after taking multiple drags and/or holding their breath - they become dizzy or even pass out. I’ve never passed out from this, but I have become very dizzy before.
A few years ago there was a pool party in Mexico where organizers dumped a couple of gallons of liquid nitrogen into the pool. They achieved the desired fog effect (condensation of water vapor due to the low temps), but the huge volume of gaseous nitrogen at the surface of the pool incapacitated several people and put one guy in a coma.
Some gases aren’t inert, but can still kill relatively painlessly. Carbon monoxide poisoning can kill at 1600ppm, but it takes two unpleasant hours. However, if you increase the concentration to 12,800 ppm, you pass out after just a couple of breaths, even though there may still be plenty of oxygen available. The old trope of putting your head in a gas oven to die wasn’t about asphyxiation due to methane; decades ago, the gas used was coal gas, AKA “town gas,” and contained a lethal percentage of carbon monoxide.
Some people are a bit blithe about painful deaths that are over in a short time.
When in agony, a short time is a long time.
Relevant previous thread about this here -