I am assuming you have significant stenosis as you did have a central cord injury based upon your symptoms and you have two surgeons who want to perform surgery. If you have no stenosis and you developed SCWORA (spinal cord injury without radiological abnormalities), this would be very rare and unlikely.
Stenosis from fracture (injury) is different from developmental (degenerative) stenosis. In fracture stenosis, you probably would have had surgery that first fateful day. WIth developmental stenosis, you don’t have to have surgery immediately but the trend of surgeons is to put you in a neck collar to protect your cord and do surgery as soon as is feasible.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.