If your knickers are tighter than your hairpiece, you're strangling the family dynasty Tim LOL.

I had my appendix removed a few months back, and had to confront this issue. I was very tempted to just wear my hairpiece and say nothing, but in the end I asked the anaesthetist and he told me it was hospital policy that I would have to remove it. However, he said he had had the same issue with other patients, and he would give me a surgical cap at the point when I would have to change for theatre, and I could tape it in place with hairpiece tape so it wouldn't fall off. He would leave instructions with the nurses to leave the cap on after surgery. So that is what I did. The cap was still on when I came around, and when the grogginess passed I was able to go to the bathroom and put on my unit again.

I think if you ask you will be told to remove your piece. I imagine the chances of the piece causing a problem are one in a million, but they just want no avoidable complications whatsoever. I would have felt very uncomfortable at the thought of lying unconscious after surgery with my bald head exposed for all to see (particularly because the white outline makes it pretty obvious I normally wear a piece), but the cap made it OK. You would need to take some toupe tape with you, as well as a clean hairpiece already taped up, so it can be put on easily and without too much fuss when you feel ready.