Right, different costumes would make that possible, but I don't see the actual point for them. At least not concerning the missions.
At the time (when you think) he's still with the MI6 he wears that black camouflage suit (or whatever you might call it).
Why would he change it? It's not like "I'm with the MI6" or "I'm with Janus" is printed all over it. It's just a cool black suit that is useful in dark areas or at night.
Even his henchmen (in the game) did wear those all the time and I'd think it would be rather strange if they wore casual wear or something like that. ^^
At least the alternative costume would have to be more than just some color changes (like Bond's different suits, although I have to admit I like them, but he's always on the same side anyway).
Regardless of whether you decide to make him playable for one or both teams: alternate costumes are cool. I wish there were more of them avaiable (and maybe linked to some achievements or whatever as discussed in the thread about achievment ideas).
As for Dr. No you're probably right... didn't think of that. :- / Well, you could also say if he managed to come back, he might have used more advanced technology for his hands by now, so he could be able to shoot a gun.
Or he could be some fun-character labelled with a warning he might ONLY use his hands for dealing damage to other players.
EDIT: You could have an achievement with that called "No, No, No, No, No!" - win the round as Dr. No 5 times (4+ players, LTK and weponsets that don't include a weapon other than knifes and slappers excluded).
(couldn't think of a better name, a scene from the movie Inglourious Basterds suddenly came to my mind -> )
Please note: I dislike the historical person of A. Hitler because of what he did and what he planned to do, but if he had chosen to become a comedian instead and get rid of his mad ideas he'd certainly been a great success in that business, because of his gesture, his facial expression and of course because of his way to speak and stressing certain words. I guess that's the reason for all the spoofs concerning him.