It's a really difficult question and I like the fact that you leave it open at the end depending on what your circumstances could be in that situation. The fact that you delved into the psychology of having to execute someone to eat and face that forever after, that is something I didn't even think of. I don't think I could live with that on my conscience either.
Nicely thought out!
Fortunately, this are only what if scenarios so we can still make decisions based on our morals and what we feel right now.