I think it is fine as it is. "Spy" may not be the perfectly correct term for this kind of operation, but as far as I know the game aims to use simple, generic names that fit a whole range of related real-life things - like with the improvement names. "Spy" is short, and it is both a verb and a noun, very practical. More precise terms tend to get clunky, you would need to replace the "Spy"-button with a huge "Conduct special forces operation"-button.
And as for the damaging and repairing of nukes, I'm not sure if this would not add too much complexity. Repairing would not be free, I suppose. Yet nukes are not all that expensive to buy, so some people would simply scrap the damaged ones and buy new. The game would have to keep track of damaged and functional nukes, so you would be able to choose which kind of nuke to scrap, and so on. Not impossible to do, of course, but I am undecided.