No, there isn't a standard medical school program in the US or most other countries that allows you to graduate without *any* surgical experience. While the amount of hands-on surgical experience varies between specialties and rotations, all medical students participate in some form of surgical clerkship or rotation. This usually involves observing surgeries, assisting with procedures (under supervision), and potentially performing minor procedures themselves.
While you might choose a medical specialty that involves less hands-on surgery (like radiology, dermatology, or internal medicine), even those specialties require a foundational understanding of surgical principles and techniques gained through observation and participation in surgical settings during medical school. Completely avoiding surgical experience is incompatible with a medical degree.