I read about a guy getting incarcerated for f*cking an old woman to death. Claimed the sex was consensual, but she had a heart attack. Still up in Folsom for raping and killing a senior citizen.
If you're looking for doom scenarios, you can always find something. And read it wrong.
There are two different types of anaesthesia, namely local anaesthesia, where only your lower body would be affected and you stay conscious, or general anaesthesia. For a procedure like a vasectomy, local anaesthesia + anti-anxiety medication is the most common, but when the surgeon expects the procedure to be complicated (for instance, with patients are over BMI 40) they choose general anaesthesia. In the rare occasions where local anaesthetic is used but the procedure turns out to be more complicated (and thus time consuming), the patient is brought under general anaesthetic.
So your fear of anaesthesia wearing off and resulting in pain is unwarranted.
Of course, your misinformation fuels your anxiety and you expect the worst case scenario, because you want an excuse not to have a vasectomy. Sorry, you'll have to find another excuse, because the procedure is never painful.
Unless you get it done in a third world country with a rusty bajonet, but I assume you'd get snipped in the US.