I doubt that it would be legal for North Carolina to outsource their executions to another state. It appears to me, strictly from a layman's opinion, that North Carolina would have to carry out its executions in North Carolina.
I would also fault North Carolina's Legislature here. They could simply enact legislation which specifically enshrines in the law that an execution is not to be construed or defined as the practice of medicine or pharmacology. Many other states have done just that. This would let the medical profession off the hook, in my opinion.