This topic reminds me of the scene in Catch 22 where Yossarian is in the bomber plane.
Snowden has been hit by anti-aircraft fire, and as he’s dying he’s saying over and over “I’m cold. I’m cold.”
Exactly. Something poignant.
You know, even if someone really wanted to make sure that no information got out, and made sure that they were seriously deaded, I would have no problem with a last gasp of that kind. It fits with the intent of the person killing them (no information) but allows some final character moment.
“I’m cold. So cold”
“I want to go home…”
“Rosebud!” (Sorry, had to put that one in there.)
Which is why you go with BDE rather than defined rules. Most people are grown up enough not to spoil things but BDE give sthe opportunity for those final calls.
What’s BDE?
Best Dramatic Effect.
Basically you go with what is likely to be cool and work with the story leaving it to the individuals to make it work.
Example would be
PC Assassin kills PC Victim, as he helps lower the victim to the floor whispers I am cutting your throat so you cannot tell anyone who killed you. PC then lies bleeding and as people rush up knows to say in a raspy voice, 'My killer was…cough cough arrghh…"
No worries about timing, as long as the victim is not being an ass it allows both the Assassin and Victim to play their roles, add to the tension as they see fit and add to the tension in the game. All it takes is a quick whisper at a time when both players are presumably quite close anyway and if the Assassin doesn’t tell the Victim anything it simply allows the Victim a bit more leeway in what they might say (noting that last words are not mandatory 
I take back what I said on throat cuts - had it yesterday done by experienced player, it was all good.