The Commander-in-chief powers are quite broad. The War Powers Resolution limits his ability to engage unilaterally in military action, by requiring him to report to Congress within 48 hours, and if Congress disapproves, troops must be removed after 60 days. However, this law pertains to armed forces, and would not apply to remotely-launched missiles. Additionally, it is unknown if the resolution is unconstitutional (presidents say it is). No law at all requires POTUS to obtain permission from someone else, in order to engage in a military action.

The Commander-in-chief powers are quite broad. The War Powers Resolution limits his ability to engage unilaterally in military action, by requiring him to report to Congress within 48 hours, and if Congress disapproves, troops must be removed after 60 days. However, this law pertains to armed forces, and would not apply to remotely-launched missiles. Additionally, it is unknown if the resolution is unconstitutional (presidents say it is). No law at all requires POTUS to obtain permission from someone else, in order to engage in a military action.

Article 90 of the UCMJ states that it is a punishable offense to "willfully disobeys a lawful command of his superior commissioned officer". The manual also states that

An order requir­ing the performance of a military duty or act may be inferred to be lawful and it is disobeyed at the peril of the subordinate. This inference does not apply to a patently illegal order, such as one that directs the commission of a crime.

Murder of a civilian is an example. It also says

The lawful­ness of an order is a question of law to be deter­mined by the military judge.

"Shocking the conscience" is not a grounds allowing disobedience. One can only conjecture how a military judge would evaluate the lawfulness of a presidential order, when there is not a shred of legal evidence that such an order is in fact illegal: I conjecture that the order would be found to be lawful.