This may sound odd coming from the psychopath who slaughtered everyone in Fallout 3 and was concerned about whether or not cannibalism counted as food (not to mention what would happen if I engaged in it openly), but I've just restarted New Vegas with the intent of playing a character who never kills humans. I'm told it's possible to win the game this way, though it will be very challenging. (Perhaps moreso since this is the character for whom I chose hardcore mode.)
Is there a way to solve Primm's problems with convicts (and specifically, both get and solve My Kind of Town) without killing any humans?