Most heated polymers are bad for health, and among them PVC is nasty.
Chlorine molecules and hydrogen chloride aren't the main concern. At heat, the atoms recombine, including with oxygen from the air, to create a vast spectrum of poisons. The monomer vinyl chloride is just one example:https://en.wikipedia.org/wiki/Vinyl_chloride
More generally, chlorinated hydrocarbons are especially toxic in fires and at heat. Most compounds of C, H, Cl are poisons, and at high temperatures there is no control on what compounds are created. You get inevitably a very broad mix of compounds, many of which are toxic.
If you inhale the stinky fumes once you'll survive with temporary eyes irritation and a headache. But if you make a regular activity of it, without protection it will kill you. Have no doubt about it.
For my personal activity, I'd completely avoid heating PVC. If you really have to do so, and worse, on a regular basis, you need a fume hood that separates any living creature from the gasses and doesn't release the gasses in the atmosphere. Plus, comply with uneasy regulations.
My feeling is that choosing and installing the adequate equipment, defining its operation, is way outside your knowledge. To the very least, you need an expert, maybe the fume hood supplier, to define it for you, which won't make it cheaper. Even that way, when unexpected situations will occur, you won't make enlightened decisions, and this is dangerous.
Every polymer containing chlorine is equally bad at heat. The same holds for polymers containing fluorine, like PTFE and PVDF. Polymers containing nitrogen (ABS being common) aren't healthy to heat neither, as they can release things like acrolein and cyanide, even if in small amountshttps://en.wikipedia.org/wiki/Acroleinhttps://en.wikipedia.org/wiki/Hydrogen_cyanide
Polymers containing only C, H and optionally O are less nasty at heat. These would be my preferred choice for laser engraving. It leaves you PE, PP, PET, POM and many more. Don't underestimate them neither.