Frame the problem around presentation. Shoulder dystocia happens in a head-first birth when, after the head emerges, the leading shoulder jams behind the pubic bone. The rescue techniques are therefore all aimed at freeing a shoulder in a cephalic delivery.
Run through the recognised drill, often remembered as HELPERR. McRoberts maneuver sharply flexes the mother's thighs onto her abdomen to flatten the sacrum and rotate the symphysis, the single most effective first step. Suprapubic pressure is added simultaneously to nudge the impacted anterior shoulder downward and forward under the pubic arch. When external measures fall short, the Woods screw maneuver rotates the fetus internally to dislodge the shoulder, and the posterior arm may be delivered.
Now spot the intruder. The Mauriceau-Smellie-Veit maneuver is something entirely different: it is the method used to deliver the after-coming head during a vaginal breech birth, where the operator supports the fetal body and applies controlled flexion to the head. It has no role when the difficulty is a trapped shoulder in a vertex delivery.
So the technique that does not belong to the shoulder dystocia toolkit is the breech head-delivery maneuver.
\[\boxed{\text{Mauriceau-Smellie-Veit maneuver}}\]