Yes, and I’m sure these will all be taken into consideration. I think though, that he should either resign his commision or obey his orders.
Indeed. The military recognizes "legitimate avenues of dissent", and the ultimate trump for a commissioned officer is resignation. I suspect that, without definitive proof of Obama's legitimacy, this would be MAJ Cook's optimum course of action, and it may yet come to that. I don't think it's MAJ Cook's point to protest the order or policy, but merely to ensure that he's not placing himself in legal/moral/ethical jeopardy by following an order that he suspects may not be legal, and consequently he's merely looking for clarification of that at this point.