Q. For clarification, how exactly do active poisons work? One lethal, one utility, both with potential to proc from both weapons?
One Lethal, one Non-Lethal, and both poisons are effectively on both weapons. Whenever you land either a mainhand or off-hand strike, you have a chance to apply both your Lethal and Non-Lethal poison.
EDIT: I think I see, in the Shiv tool-tip. It says 25% weapon damage (far less than 200!), dis-enrage, and a concentrated form of your active non-lethal poison.
It's still a weapon strike, you'd think it'd still have a chance to apply a poison, even if it isn't guaranteed.