I agree with the idea of the Composure test, I think it fits well. Faced with death, combat situation... probably the same thing (it's your Quality so it's your call).
I think that a -1 to all social tests is a bit much, though. Or a bit too much of a blanket effect to represent what you're going for. Maybe get him to pick up an additional Quality like Flashback or Addiction, like MadMaddy suggested.
If you want the social penalty, maybe narrow it down a bit to any social test during a 'run.