Executive orders are made to help amend and enforce laws. Once UBCs are in place, an executive order can be placed to amend the law allowing registration as they will simply need to show registration is required to enforce UBCs.
One would hope that Coburn or someone else would insert specific language forbidding registration into the law. It is already law that a registry cannot be created. I mean can an EO just violate the law in order to enforce it?