It is a logical error to change what you are talking about in the middle of your argument.
Your initial point was not against the executioner, but against the possibility that a judge could make an error which will lead to the death of someone. That error is not deliberate. Your argument is logically wrong.
Is it a murder? No, it's not, even if the person is innocent. A murder is the unlawful killing of a human being, it has nothing to do with the concept of innocence. A soldier who kill an enemy combatant is not committing murder. A lawmaker who decide that a kind of crime should be punishable with the death penalty is not committing murder. A judge who come to the conclusion that the crime of someone is subject to death penalty is not committing murder. An executioner who kill someone condemned to death penalty is not doing something unlawful, so it's not a murder. Again, your argument is logically wrong and saying "in fact" won't make it magically true.
Finally, if every single rational objective that can be applied to death penalty was also applicable to life sentence, everybody would be satisfied with a life sentence and nobody would ask for the death penalty. You just choose to ignore the obvious because you're irrational.
Behind all the excuses and false logical arguments, the only real reason against death penalty is exactly the same as being for death penalty : it's purely an emotional reason. The basis of all our moral constructs are our emotions. As long as people will try to justify their little emotions using dubious arguments, this debate will never end.
Yes, I know being rational is not the strong point of humanity. But it's not because you're irrational that I should be!