Step 1: Picture the layers at the front of the wrist.
At the wrist, the flexor retinaculum is a tough band that roofs over the carpal tunnel. Some structures lie deep to it, inside the carpal tunnel, and some lie superficial to it, just under the skin. A superficial cut only reaches the structures in that shallow, superficial layer.
Step 2: Place the ulnar nerve.
The ulnar nerve does not pass through the carpal tunnel. It runs superficial to the flexor retinaculum, through Guyon's canal, alongside the ulnar artery, on the medial side of the wrist. A superficial cut across the wrist would injure it.
Step 3: Place the palmar cutaneous branch of the median nerve.
This branch leaves the main median nerve a little above the wrist and travels superficial to the flexor retinaculum to supply skin over the base of the palm. It is superficial, so a shallow cut would injure it too.
Step 4: Place the superficial branch of the radial artery.
The superficial palmar branch of the radial artery crosses the wrist superficially, often over or through the thenar muscles, to help complete the superficial palmar arch. It lies in the superficial plane, so a superficial cut would damage it as well.
Step 5: Place the median nerve trunk itself.
Unlike its cutaneous branch, the main trunk of the median nerve travels deep to the flexor retinaculum, inside the carpal tunnel, together with the nine flexor tendons. Because the surgeon specifically noted the cut was superficial, it would not have reached the median nerve trunk lying deep to the retinaculum.
Step 6: Final conclusion.
The structure that would NOT be damaged by a superficial wrist cut is the median nerve itself.
\[ \boxed{\text{Median nerve}} \]