Continuity mistake: In the flashback to the Watchmen's initial meeting, the Comedian lifts his cigar to his mouth, but in the next shot, both arms are down by his sides. (00:43:10)
Continuity mistake: When Veidt is explaining how he offed the Comedian and killed the fake assassin, Rorschach launches an attack behind him which Veidt blocks, the shot changes in an instant cut and Veidt is now facing Rorschach. (03:00:35)
Answer: He has spent years as a costumed vigilante despite the fact that it was illegal. He has a very strict idea of what is right ("never compromise") and has proven himself incapable of doing otherwise. So no, there was no real chance of negotiating with him - Rorschach himself made it clear he'd have to die if they wanted his silence.
Garlonuss ★
Death was not the only choice. Doc M could easily have teleported/banished Rorschach to Mars/anywhere secluded in an oxygen bubble. He could have spared his life and just made him mute or manipulate his brain chemistry/atoms to remove the memory of what happened. The point is Doc M is all powerful and could manipulate matter at his whim; death was just a plot device creating a chance of an emotive martyrdom/sacrificial ending.
Ethically speaking, exiling him to Mars or erasing his memory of the event can be considered just as cruel as killing him, because then his agency is being taken away from him. Rorshach's malcontent with the situation poses a problem for the other heroes, and since Dr. Manhattan isn't willing to let him tell the truth of what happened, he obliges Rorschach's demand that he kill him instead.
Phaneron ★