This is weird and it's nonsense. Obviously Leonardo is the captain. First Officer would have to be Raphael, arguing with the captain's decisions then giving in. Donatello IS an engineer, so that's clearly his job. And that only leaves Michaelangelo to be the doctor. ...Don't get too injured, guys.
Agreed, none of them would make a fantastic doctor. I was trying to think of what role Mikey could fill, and honestly I don't think he's grown up enough to be any kind of senior officer. Cowabunga, lower deckers!
Makes sense having Michaelangelo as the cursed chief engineer if you consider "The Last Ronin" storyline. Splinter and his brothers are murdered, so Mikey uses all their weapons/styles to seek vengeance.