Local is no biggie, but it depends on the person. I had a surgery on my Adams apple under local and I was happier than a lark the whole time, haha.
Two surgeons have told me it's actually better to do local, because the doctor is more careful and also it is faster for the body to process the anesthesia vs general which takes longer and puts you out more heavily in the days following. I don't think it necessarily affects the result, but it will probably have you back on your feet faster.
Sorry I don't have any experience with the specific surgery you're talking about, but that is what I know about local vs general. Hope it helps!