It is perfectly acceptable to work out your options with the urologist and the anesthesiologist and then PUT THEM IN WRITING.
You can outline choices, in order of preference and include "if this, then" options that are consistent with what they would normally do anyway and/or what they've agreed upon. The real purpose is to clearly record what was agreed by everyone so there's no "bait/switch" when there's no turning back.
Be careful not to list anything as "NFW - no matter what" because any responsible physician can't be put in that position if it ends up your life is at risk. Their malpractice insurer could refuse to insure them for your case, or refuse to cover them if you (or your estate) sues them, even though they explicitly followed the agreement. One way to protect everyone is to make sure that you have someone PRESENT with medical power of attorney (or state equivalent) who can be consulted before they resort to a general (assuming there is time and you're not dying).
Just for context, I'll add that there are many, many hospitals that will directly ignore an Advanced Directive, DNR and similar restrictions out of fear of litigation. [Sometimes the staff will admit it, sometimes they won't.] I've had this confirmed a number of times in discussions with ICU, CCU and Cardiac nurses. The hospital's argument is that they can be sued if you die, but not if you live - even if living becomes a living hell for you. This is not the same, of course, but the hospital's policies should be checked, as well, and that's my point. Physicians have to respect hospital policy (to a point) in order to preserve their privileges at that hospital. If the surgery can be performed in a surgery center, you would probably have more certainty about how that all can be managed to your preferences.
(Note: I am not a lawyer and this is not legal advice. I do work in health care management consulting and am familiar with these matters. In addition, I have served as a P of A twice for relatives.)