Can general anaesthetic and the healing process from surgery affect a new hair transplant?

The Internet is a not a place for personal medical opinions.Even if it is, you should trust the doctors that will be doing your surgery.If a second medical opinion is what you are seeking you need to actually ask the doctor in person.A doctor that can examine you and take your full medical history.There may be other issues you are not aware of.Hypothetically if another doctor said the anesthesia may affect your transplanted hairs, would you not have surgery and continue to suffer from bunions?

At 3 weeks, grafts have committed to either growing or not growing and surgery is unlikely to have any negative long term effect. That said, one needs to keep in mind that any surgery with general anesthesia can rarely cause temporary shedding. We call this telogen effluvium.  Telogen effluvium is not common after surgeries involving general anesthesia but most certainly can occur. If it does occur, patients develop shedding 2-3 months after the surgery. It lasts a few months and then hair grows back. Reference of InterestTelogen effluvium following orthognathic surgery.Lypka MA, et al. J Oral Maxillofac Surg. 2007.

General and regional anaesthesia will not have any effect on your hair transplant. Good luck with your bunion surgery, I hope it goes well!