Not likely but you can ask. Sometimes orthopedic surgeons work with anesthesiologists who use acupuncture instead of anesthesia. Surgery is rarely done without an anesthesia and for good reasons. If the patient suddenly feels pain and jerks away, the surgeon's knife or other tools can sever (cut) a nerve or blood vessel.
Some of the structures in and around the knee are very sensitive. Others are not. At least one surgeon mapped the sensitive structures of the knee without using an anesthetic. The doctor did this to himself. He probed his own knees without anesthesia.
He found that the fat pads were very sensitive tissue. So were the synovial tissues that protect the joint. The joint surface itself and the cartilage weren't very sensitive. The bone just under the cartilage was very painful when overloaded. This happened most often when the cartilage was damaged.
All in all, even with a high tolerance for pain, it's probably best to be numb when this operation is done. Too many things can go wrong when a patient isn't anesthetized.