You should approach this question by finding a surgeon within your network and then go in for a consultation. If you decide this is a good fit for you, advise the surgeon that you have been approved by your insurance already. In many cases, the insurance company will simply reauthorize the procedure to be done with your new surgeon.
Finding an in-network surgeon
Generally speaking, when your surgeon submits an insurance approval it is for that specific surgeon. Some insurance companies can be pretty reasonable about switching the approval, especially to an in-network surgeon since it will likely cost them less. Other insurance companies are a vast legion of people who seem like o be trained to be unhelpful. The best approach is to find the surgeon you like and then this surgeon can explore the transfer of the approval for you.
I would caution you about two things:
1. Depending upon your plan, the number of experienced and qualified surgeons in your area may be VERY limited.
2. If you find a surgeon who is in your network, make certain that the anesthesiologist and the facility are as well. Otherwise you may get an unpleasant surprise.