Well the death caused from the air in the heart would seem natural.
Injecting air into their plural cavity would work almost as well. But that would be excruciatingly painful. So if they passed out drunk on the night of the event, it would be a lot easier to inject air in between their ribs and most likely cause Pneumothorax and collapse both lungs in a matter of minutes.
well, if you want to really get someone, bind them in cloth. make sure there is a whole where the can piss from. then continuously have them drink water. they will lose electrolytes and minerals they need to survive.
from the severe lack, they will die, plus it will look like they simply fainted.