What kind of surgery. Types of anesthesia are local light sedation by rn; deep sedation, nerve blocks, spinal, caudal , epidural and general all by anesthesia providers. None of these is always the safest and each one may be the safest for you depending on your medical condition and type of surgery. I would not use any other things like hypnosis or acupuncture for any surgery.
Local or regional. I assume you mean general anesthesia - its always a good idea when having surgery to go with local or regional anesthesia if at all possible. Local or regional today is very safe and reduces the risks and possible side effects of general anesthesia.
Talk to MD. There are some operations that are done without anesthesia, but i need to know which ones you are talking about before i can be of much help.