

Upfront: it should be obvious that no sane person wants us to drop a nuke or thinks there’s any connotation of “okay” to any aspect of it.
Why do you think it would be an illegal order? There are very clear rules on what makes an order legal or not and, horribly, attacking a nation that poses no real threat isn’t on the list. What nations we attack is a policy matter, and the rules are very clear that the military doesn’t get a say in policy.
Explicitly targeting civilians for a strike on a city is where the line would be. Targeting something else in the city and deciding the civilians are acceptable collateral damage is right on the line. Legally, it’s entirely unambiguously evil morally.
There are checks that keep the president from unilaterally launching a nuke. Unfortunately, the intent of those is to ensure the president is legally competent and actually the president, not to ensure he’s wise or rational.
https://en.wikipedia.org/wiki/Harold_Hering
The system has been explicitly designed to minimize the risk of conscience preventing a launch. Issue training orders where the firing crews have no idea if it’s real or not. Keep them on two week rotations where they don’t have access to the outside world so they wouldn’t know. Specifically select for people who will follow the order because it’s validcand legal, without considering the greater context. People who are legitimately confused but ultimately unconcerned with protests against them specifically doing what they do, including clergy from their own religion. (Actual story of an ICBM operators reaction to nuns protesting and attempting to block access to the missile site he was stationed at)
There is no doubt in my mind that if the order were given and the VP and cabinet didn’t remove him, that the order would be followed.
Don’t get me wrong, it should be illegal to do a preemptive nuclear strike, it just sadly isn’t.
It might not be feasible for the entire chain to have the information needed to make that call, but there is definitely someone in military authority positioned to know if it’s defensive or offensive, and that person should be both allowed and obligated to refuse the order if it’s an offensive strike.
Morality and the law may not be equivalent, but it would certainly be more convenient if they were closer.