I could see Klugman as McCoy.
Anne Francis as Janice Rand (Going along with the early idea that she was supposed to be the regular female lead.)
Bruce Lee as Sulu (He'd need more fight scenes.)
Eartha Kitt as Uhura (Not sure if she ever did regular weekly TV gigs, but she would have been purrrrrfect.)
And, if they'd conceived the character for Season 1 and gotten the actor before that other show did...
Davy Jones as Chekov