>What I meant by “whipping a punch” was basically involving your shoulders in the punching motion. Snapping your shoulders like a whip as you’re extending your arm to punch seems to also give it more force.

The whole body should be involved, toes to knuckles. A proper punch or kick involves almost every muscle in the body, even the ones in the non-striking arm or leg. That's why proper technique has a twisting motion to the hips; you add the momentum of the entire upper body, not just the arm reaching out to strike. In my experience, setting the upper back solid when striking seems to make the biggest difference in the amount of force delivered as it provides a kind of backstop to the shoulder as the force of the strike is being transferred. If you don't keep your shoulders solid, and have good arm alignment when you strike, the force generated by your legs and hips goes into bending your wrist or shoulder instead of transferring into your target.

Wrist rotation is not 100% necessary; it's a technique I've encountered in some martial arts and ignored in others with no discernable difference in speed or power. I've personally had better results not rotating the wrist as I seem to have better alignment without rotation, but that may be a practice thing. It's also easier to get boxer fractures of the ring & pinky knuckle with a horizontal fist than it is with vertical or slightly angled fist. The slight gain of the twist (which is in itself debatable) is easily offset by having good alignment of the bones when striking.