Doctors and the Death Penalty

Should doctors be involved in capital punishment? Currently, doctors reject the death penalty, as participating would violate their Hippocratic oath of doing no harm to their patients. The American Medical Association prohibits doctors from being involved, except for when writing death certificates. Some people though, believe that involving doctors would make death be a smoother process that would be less painful for the person being executed. Also, the fact that doctors are not involved makes the actual process of someone being executed have a high risk of being botched. The people involved in creating these methods are not doctors, and thus do not have much expertise on how to do it correctly or in a manner that causes not much pain.
Personally, I am against the death penalty, but the manner in which people are being killed is very troubling to me. I understand the ethics that make doctors not want to be involved, but this has made executing people a very messy process. I also understand that the ideal of the death penalty being removed from the US justice system is unlikely since the majority of people in the US support it. At the very least I don't think that it is ethical for people to be killed in this manner, but is it even more unethical for a doctor to facilitate it?
I think that lethal injections need to be rethought, and have the American public educated on what the death penalty actually entails. Like how the fact that the death penalty does not deter crime, and innocent people are still being killed by the US justice system in this manner. That the death penalty is often unfair to people who have been abused, have a mental illness, and/or intellectual disability. I think that by re-educating people, maybe the death penalty can be rethought out.

https://deathpenaltyinfo.org/stories/lethal-injection-and-physicians-state-law-vs-medical-ethics
https://www.youtube.com/watch?v=0lTczPEG8iI