On more than a few occasions have cut myself doing woodworking projects or working on the house. On at least two occasions I severed nerves in the process. In all those times, pain was not an immediate sensation. Pain came later, sometimes in a minute and some well after the incident. About 25 years ago, I was hit in the back of the head by a falling telephone line on a construction site. I never lost consciousness. I was obviously stunned, and only after, maybe, a half minute or so even began to realized I was hit. 45 years ago working as a security guard at a factory, a man making packing crates severed a portion of his hand with a table saw. For whatever reason no ambulance was called and I took him to the hospital. When I picked him up in the shipping department his hand had been severed for a good 3 to 5 minutes. People were asking him about pain and he was very alert and stated he had no pain and he felt good, good enough to walk to the car under on his own (two of us held his elbows just incase he fell.) It was only in the car with me on what was probably a ten minute ride to the hospital that the pain started to set in, and then he became woozy and was about to pass out. I had to get emergency room attendants to help him. I realize that any of these are far cries from having your head separated from your body, but maybe there is just not enough time for any sensation to set in. As stated by someone earlier, the body won't feel anything as it needs the brain to feel pain. I think it is quite possible that even if consciousness persists, the brain may be too stunned to feel anything before the rapid bleed out and loss of oxygen would lead to unconsciousness.
That reminds me of the mad doctor who dedicated his life to science by telling the world what cyanide tasted like. He muttered something about almonds as he died, but no one has ever confirmed his findings.
if you don't have that choice, you probably won't know it until death is imminent anyway. unless you're on death row or something.
There are cases involving past life experience (or reincarnation) in which the person remembers being on death row, executed, only to be reborn in another body. Perhaps someone in a past life was beheaded and remembers the experience in sordid detail.