I would say do what you feel you must. Just remember that you are acting as agents of The Five. More than likely they would pay to have Mani raised if your PCs feel the need to kill him to keep him from hurting others. However, they might make the PCs pay that cost, if they feel your characters acted rashly.
Mani is what he is in the end. He is a killer and gets joy from seeing death and blood. While the first death he caused was about self-preservation, his attack on Odhran was (more than likely) an impulse of his unstable nature. Yes, he might be trying to provoke Big Tim or Breva to end him quickly, or he could just be crazy and evil.
Of course, in a world with spells like raise dead and resurrection, Odhran can be brought back to life if his soul is willing. If his family can't afford it, the commanders of the Regulars might pay for it and extend his time in the guard until the money is paid back. That assumes, of course, he isn't a career man. If he is and is brought back to life, someone else in his family might have to become a new recruit until the money is paid back.
Remember that most of the Bluffside guards (especially the Elite) assigned to the Old City district are the sons and daughters of noble families or merchant houses. There are some from the New City district too but most of those guards are assigned to New City or the Temple District.
In the heat of the moment, the PCs might not care about the facts. I won't lose much about the ongoing story if Mani dies.