The recurrent laryngeal nerve is most at risk during thyroid surgery because it runs in close proximity to the thyroid gland, specifically near the inferior thyroid artery. Injury to this nerve can lead to vocal cord paralysis, causing hoarseness or airway compromise. Surgeons must carefully identify and preserve the nerve to prevent postoperative complications. Unlike other cranial nerves listed, the recurrent laryngeal nerve lies within the surgical field during thyroidectomy, making it the critical structure at risk. Preservation of this nerve is essential for maintaining voice and airway function.

Reference: Gray's Anatomy, 42nd Edition.