What are the possible implications if I wait for a couple more weeks to have the procedure done?
What damage can result if my liver enzymes continue to be elevated before I have surgery?
Since your doctor told you that you shouldn’t wait and after all he is the one who is an expert for this than you should probably listen to him.
Anyway elevated liver enzymes don't signal a chronic and serious liver problem so maybe there is no need to wait and post pone your procedure. Did you consider that maybe you are just trying to find excuse for reschedule the procedure because you are afraid of the operation itself?
After the procedure you will be monitored so that nothing can go wrong and you shouldn’t be afraid of this. And if you are by any chance sensitive to anesthesia than ensure than someone is with you when you wake up. Let us know how everything went.