I have had two outpatient surgeries while wearing, and I never told them I wore a piece and it was never a problem.
The first time I got the twilight anethesia and don't remember wearing the surgery cap.
The second time was a little more involved, and they did give me a hair cap to wear during the procedure.
I don't think you will be in any shape to bring tape and put your piece on as someone previously suggested.
I say just wear it unless you are getting some type of head surgery.
Just my 3 cents.

Tina

p.s. hope all works out well for you!