He is Commander in Chief.
He can issue orders.
It should be in the form of a DoD Directive.
It is a simple staff job. Any competent O-3 should be able to do draft an effective DoD Directive to do the job.
It is Defiance by Compliance at the upper levels of the DoD.
President Trump's order would subvert 70 years of propaganda and indoctrination in our Military.
That is one of the reasons it is so important and needs to be done.
It would have to be an Executive Order, which POTUS has complete constitutional authority to do.
But I would NOT be in favor of everyone toting guns openly. Only officers and NCOs: the key being the NCOs because they need to be re-empowered and separated from the non-rates. Yes, the term non-rates needs to make a comeback.