That feels like a very constructed question. In all likelihood, nobody would care and you could just pick.
What a judge would decide if you were fined by either spectrum authority and appealed that fine is only known to the hypothetical judge.
Whether or not you're in violation of code so that they'd fine you is in the end subject to interpretation by the spectrum authority, which might consider you on their "side" if parts of your activity do happen on their side. Which sounds likely, given that borders are infinity thin imaginary lines, and operators are not. Whether the responsible person in that authority seems that a relevant beach of code is, again, known to nobody but that hypothetical person.
Again, realistically nobody would know or care,
Also, reminder that sending your identification has a simple purpose: identifying you, and either choice will. It's thoroughly irrelevant whether you're 5m south or north of a border to radio propagation, so there is no practical advantage to being overly specific, either.