WildRose is correct, "Swat Snipers" who go outside of Dept policy, rules and mandates, or State Academy standers based on the States sniper training certification program, who set the State standers for snipers, do so at their own risk, and you will pay the price these days.
As for whether they'll know what ammo you used, yes... they will.
Remember; Swat snipers are not alone wolf snipers, you are part of a team and you have a spotter, and in most cases, there are multiple Swat sniper teams on the scene.
Your cartridge or cartridges will be policed up after the action as evidence for the coroners' inquest if a death is involved, it's not like our Military snipers.
As for specialty and/or sanitized ammo the only place I am aware of it is in the military units, special operation... and yes, now and then they still do when they don't want to leave a calling card and can't pick up their brass... or the whole operation might be sanitized, so the ammo would be as well. Things like "wet works" operations is the first thing tha comes to mind here, which Swat sniper would never do, or at least to my knowledge they wouldn't... and I was in the game a long time. Ok... here's a photo of a 7.62x51mm NATO sanitized cartridge as a FYI Cheers