Far from being a legal requirement, the RN historically has a very disappointing history of carriers being commanded by big gun or small ship admirals/skippers and seldom by naval aviators to the detriment of the aviation contingent. Their operational failures for this reason are legion and part of the history books. Worse, it now looks as if the new "carriers" air groups are to be "led" by Air Force rather than Naval commanders.
Wow. That might work in the UK, but having black shoes command the carrier and Air Force pukes command the air wing on the carrier and each has their own island on the ship just would not work in USN. Interestingly, the ship guys and aviation guys aboard those ships would not even have a common uniform. The only difference in USN as that the ship guys and aviation guys have different colored shoes, and that was enough of a problem that one of those infamous Z-grams from CNO Zumwalt banned brown shoes for several years.
I wish you guys well, and you might be able to make it work, but this sounds like an unworkable set up to a guy from across the pond.