You can always keep it simple when you need someone to die dramaticly.. At the cost of being a little cheap, tell the healer that the person is beyond the help of anyone but a major medical facility right now. Tell them that they can make a test to make the man die conforbly, but that there's no real way to save him.
Most players understand when something happens to an NPC and it's for dramatic reasons. Some players will feel cheated if their healer can't save the person, but just assure them that you can't save them all.
IE: "You come across a courier standing over the bodies of two unknown men, but it looks like they got him pretty well too. Blood stains the whole front of his bullet riddled armor and flecks his lips as he takes a shuddering breath.
'Hey Chummer, need a job?'
He ask with gallows humor, his own life already spent, the only thing keeping him alive his rapidly failing cybernetic enhancements. With aid, he might live for half an hour before death peacefully clams him. Without, he's going to die in agony before he finishes the cigarette he's trying to light with a broken hand."
This is the "DM Fillibuster" method. It introduces the setting and certain immutable facts: The man's dead. But it also gives them things they can do, and makes the medic/healer useful. (Keep him alive longer to give them more information and maybe a point of Karma for letting another shadowrunner die easy, job handed off and in a haze of painkillers.)
Or you could always go crazy, and let them save the man if they really try. Just have him too weak/wounded to finish the job in that case, and maybe show up later walking with a cane or on a new cyberlimb.