Having an anasthetic carries some risk. How much? How many people per million suffer the adverse outcome you fear?
Now compare that to the risk of day to day life. How much has the risk increased?
There's a bunch of stuff you do that you don't need to do that carries more risk than anaesthetic.
It's fine for you to chose your medical care. You might want to investigate an "advance health care directive". Having one should persuade doctors that you have spent time thinking about this and it is your sincere and considered desire to ignore their advice to have anasthesia.