Vigilante Justice and its Risks

There has been debate recently between certain rabbis over whether an individual can harm or kill a terrorist who has been neutralized e.g. handcuffed.

Rav David Stav, although agreeing that terrorists are deserving of the death penalty, raised two arguments against killing a terrorist who does not pose a current danger:

1. From a practical standpoint- what will the world say if they see Jews killing prone and handcuffed terrorists? It would likely lead to further murders of Jews.
2. From a Jewish and moral perspective-: "it is important to preserve our moral superiority; [we must] not harm those involved in murderous acts who have already been neutralized and do not represent a threat.” 

On the other hand, Rav Shmuel Eliyahu said that the Jewish law is clear that we should not let murderers live. It is our lives on the line here. “We can’t be consumed all day with what others are thinking about us,” the rabbi concluded. [note- In the articles I read he brought a proof from Moses's killing the Egyptian that was striking a Jewish man. I don't understand that proof because a) we typically do not learn halacha from before the Torah was actually given at Mt. Sinai, b) the Egyptian was not neutralized, but was in the act of striking the Jewish man.]

In a later interview with Arutz 7, Rav Eliyahu said that "Rav Stav is telling [soldiers] not to shoot to kill the terrorists." Something which I think misrepresents Rav Stav's position.

Also, Rav Ben-Tzion Mutzafi, when asked by his students whether, if a terrorist has been injured and incapacitated, it is permitted according to Jewish law to kill him responded that “It is commanded to take hold of his head and hit it against the ground until there is no longer any life in it... Do not listen to Stav, for the one who is merciful to the cruel will end up being cruel to the merciful.”

I do not understand the position of Rabbis Mutzafi and Eliyahu who say that Jewish law is clear that you can kill a terrorist after he has been incapacitated and poses no threat. Even if the halacha is clear what should be done to a murderer, we have many cases in Jewish law where meta-halachic considerations apply and we do in fact take into consideration what the rest of the world will say (e.g. darchei shalom / aiva, darchei noam, dina d'malchusa dina).

Also, the mistaken vigilante killing of an Eritrean man after the terror attack in Beer Sheva, seems to support the position that individuals should not take the law into their own hands but let the justice and political systems operate. (Even if the outcomes of those systems are frustrating we have a ballot box to change that.)