Are you 100% sure that they are the murderers? Both of them not only one of them?
If one was proved to be mentally unfit to understand the difference between right and wrong and was doing what he was told (not that I am saying this is definately the case), would you still execute both of them?

You still haven't answered the question about what to do in the event of a miscarriage of justice. Are you willing to die yourself if your actions in implementing the death penalty led to the death of an innocent person, despite my persistant warnings? In my view you are already guilty of attempted pre-medidated murder of person or persons unknown.