Is there a reason why they're planning to extract them at age 15 rather than later on? Sometimes its easier to remove them before the roots start to form too soon so they're smaller to get out.
I had all four of my wisdom teeth removed under general anesthesia. I fell asleep within 15 seconds from when they placed the medication. Then I woke up in the car when my dad went to pick up my prescription medication.
General anesthesia is pretty safe overall. While there's always risk, there's risk in everything we do from crossing the street to what we eat at a restaurant. I don't consider general anesthesia to be particularly more dangerous.
My wisdom teeth are at a clearly visible route to impaction and according to my oral surgeon need to be taken out before the start of my Sophomore year.
They are not impacted and I do not feel any pain whatsoever. In fact, a quick check in the mirror and I can't see a thing different about where my wisdom teeth are supposed to come in.
However, it is true that everything we do in life has a risk. This makes me feel much better as my family is only doing it for my wellbeing and I really have no say in the matter anyway.
Everyone's wisdom tooth extraction experience is different. All four of mine were impacted and I opted to stay awake during the procedure. I was in and out of the clinic in less than 30 minutes and went to a party a few hours later. You're in good hands with an oral surgeon. They do that procedure all day every day and there are rarely any serious complications.