No, the Soldier cannot decline and the leader is under no obligation to do the corrective training with the Soldier. Frequently leaders will do the corrective training with their Soldiers to motivate and inspire them. Army Regulation AR 600-20 and FM 7-22 provide specific guidance on the use of physical training as corrective training.
AR 600-20 paragraph 4-6:
Corrective training must be related to the offense, oriented to improve the substandard performance, Can be after hours, can only be implemented until the deficiency is corrected.
AR 600-20 paragraph 4-20:
When authorized by the chain of command and when not unnecessarily cruel, abusive, oppressive or harmful, the following do not constitute hazing: administrative corrective measures including a reasonable number of repetitions of authorized physical exercises.
Corrective training is often used incorrectly resulting in over training or overuse injuries. These sessions are not smoke sessions. Authorized exercises include: Rower, Squat Bender, Windmill, Prone Row, Push up, V-up, Leg Tuck and Twist, Supine Bike, Swimmer, 8 Count Push up. Only these exercises may be selected. The number of repetitions should not exceed 5.
Word of advice
It may be easier to knock out a few push-ups rather than give an NCO a lecture about appropriate corrective training and then get corrective training that takes a few hours from your day. Be careful what you wish for.