I'd like to make one more point about nukes and "missiles capable of carrying a nuclear warhead".

The critical mass for a gun-type weapon is approximately 22 pounds of Uranium 235 or Plutonium 239. Even I, a librarian, could rig up a way to slam two pieces of fissionable material into a critical mass within a tenth of a second. Let's say that this, plus the container for the all the stuff, adds 50 pounds. The total weight is now about 75 pounds.

I can make a rocket myself that would lift that payload. With materials readily available to me, right here at home.

The problems come in making the missile accurate and to give it a range beyond a few kilometers, not in making a missile that would lift the warhead.