Not quite. The Companions are, like the Queen's Guard or the Defenders of the Stone, the closest thing to a professional national army. They're are not a separate but elite force like the Foreign Legion. The rest and bulk of the army is the retinues and levies of nobles. So just as Captain-General of the Queen's Guard is the top military office in Andor, so is First Captain of the Companions in Illian. According to the Companion, the Companions are the only standing unit.

In discussing the symbols of rank, it says THE First Captain has..., THE Second Captain has..., Lieutenants have..., under-lieutenants have...
So I think it's as clear as can be without a direct statement, that the Second Captain is a singular office.

He's on a TV show. While that would be true in the books, TV shows, and Sanderson, seem to equate rank with hand-to-hand skill. eg Gareth Bryne's blademastery coming out of nowhere. That, plus the point that they ARE an elite unit, deployed to the schwerpunkt, as it were, as well as the King's bodyguard, in addition to his private army, makes them more like the Kingsguard in aSoI&F, where hand-to-hand should be as important as the normal qualities that recommend promotion. It's like Gawyn, who has to train to be both war minister and bodyguard.

And in general, Tam faced prejudice in his rise through the ranks due to his foreign birth, which is thought (in-story) to have prevented him from being named First Captain.

All in all, to me this suggests that he would not have risen so high without considerable skill. If his blademastery was merely technical or minimal, they'd find excuses to keep him back.