Is the death penalty a viable option under the premise that assuming we have apprehended the guilty party, the guilty party, when executed, will never be able to kill again and therefore society has been made that much safer?

I think that the problem with that argument is that we can get nearly the same level of safety by sending the killer to jail for life. And given the imperfections of the justice system, there's a chance that we could execute an innocent person which is much worse than sending an innocent person to jail for a few years. Perhaps, if we were absolutely certain someone was guilty of murder and we had good reason to think that the death penalty had a significant deterrent value in preventing future murders it could be justified. But the deterrent value of the death penalty has been questioned in recent years.