If you have confidence in your Physician I would follow his/her recommendation about the surgery. If not, then may I suggest you get a second opinion from a Breast Specialist / surgeon.
Hi. Did the doctor perform some other diagnostic procedures like mammography or breast ultrasound before deciding on the surgery? If such procedures were performed, what were the results? How big are those cysts? Are they causing other symptoms like pain or nipple discharge? Pardon me if I'm asking a lot of questions, but if you can provide some of these additional information, it will help determine if the surgery is really necessary at this point. For example, if the breast cysts appear to be benign lesions on mammography, then a less invasive procedure like core needle biopsy may suffice, or maybe there's an option to merely observe the cysts for a while instead of excising them immediately.