Can a NCO make a Soldier use nair to remove facial hair?

There's a product called magic shave that's basically the same thing, it's a depilatory cream, specifically used by people who have razor bumps issues.

But this NCO is setting himself up for some serious blowback in multiple ways. This Soldier also needs to make sure he stops pushing back his appointments

To answer your question, no.
Additionally, I find it extremely sad that there is someone in our ranks that legitimately thinks that nair would be a viable option.

This NCO is not a medical professional. If said soldier is having derm problems then he needs to go to sick call to be seen. Let medical do their thing. Temporary shaving profile on record while they sort it out and NCO accept what medical says as they are the ones in charge at this point.

When the NCO decided to make the soldier do something for a medical condition he has no tried to practice as a medical provider and also could have caused harm to the soldier. I get it he is upset the soldier is not meeting the grooming standards and it sounds like the soldier is not doing their part to make sure if they can’t meet the standard due to a medical issue to see a medical provider.

In the end though the biggest blame and harm is going to come to that NCO in this situation.