when a muscle crosses a joint it acts on that joint. during the basic karate punch when the fist is chambered either on the hip or in the upper position just below the pectoral group, the prime movers of that arm would be pectoralis major (flexion of the humerus), the anterior musculature of deltoid (flexion and medial rotation of humerus), coracobrachialis (flexion of humerus), biceps brachii (flexion of humerus[minor]),pronater teres and quadratus for the corkscrew motion at the end of the punch. the triceps would be a minor player in stabilization and extension of the forearm along with anconeus which assists in extension and pronation.
on the other hand.....a classic backfist strike where the hands are held up, and the lead hand is used for the hit.....the tricep muscle would create the speed and snap for the power.