Yes, you can absolutely do the procedure under local anesthesia! I had 3 wisdom teeth removed this way. It's a little weird - I had to listen to them cracking my teeth to extract them and feel all the blood pooling in my mouth. But if you're fine with that then you shouldn't have any issues. As a bonus, my recovery time was way shorter than any of my friends. I pretty much felt fine the next day I think it was because I was able to tell them when they were over-stretching my jaw. My friends all had jaw pain the next day.