A lot will depend on how well the actors can re-create the characters that are indelibly stamped with the personas of their originators: Robert Vaughn (Solo) and David McCallum (Illya). That's the boon and curse of series television: In the audiences' perception, the actors become the characters, and they are inseparable. The actors in the remakes not only must play the characters, but they must also play the actors who played the characters.
For some good examples of doing this well, in the rebooted Star Trek films, Zachary Quinto not only plays Spock but Leonard Nimoy playing Spock; and Karl Urban plays DeForest Kelley playing McCoy.