Step 1: Define shoulder dystocia. It is failure of the anterior shoulder to deliver after the head, due to impaction behind the maternal symphysis pubis, and it is an obstetric emergency in cephalic delivery.
Step 2: Recall the standard maneuvers. First-line is McRoberts maneuver (hyperflexion of the maternal hips), combined with suprapubic pressure to push the anterior shoulder under the symphysis. If these fail, internal rotational maneuvers such as the Woods (corkscrew) maneuver and delivery of the posterior arm are used.
Step 3: Identify the odd one out. The Mauriceau-Smellie-Veit maneuver is a technique for delivering the AFTER-COMING HEAD in a breech (vaginal breech) delivery, not for a stuck shoulder in a cephalic presentation.
Step 4: Apply the exception logic. Since the question asks which is NOT part of shoulder dystocia management, the answer is the breech head-delivery technique.
Step 5: Confirm. Suprapubic pressure, McRoberts, and Woods maneuvers are all recognised steps in the shoulder dystocia drill (HELPERR), whereas Mauriceau-Smellie-Veit is not.
Hence the answer is the Mauriceau-Smellie-Veit maneuver.