Doing some basic math in my head, I figure the probability of another nuclear detonation is a function of time and the existence of nuclear weapons:
While nuclear weapons exist, the probability that another one is dropped approaches 1 with the passage of time
And so it's imperative that, in the future, nuclear weapons are wiped completely from the earth.
Is it as simple as this?
And you have a magic wand that can get rid of all nuclear weapons?
A U-235 weapon does not require any great sophistication so long as you're willing to accept a few percent chance of failure. If you just take the pieces in your hands and slam them together you have about a 50% chance of killing a city. The faster you manage to push them the more reliable it becomes.
Obtaining that U-235 is the limiting factor but it's not really all that limiting. Figuring average concentrations I own enough U-235 to make a bomb--admittedly it would take a lot of refining to separate the uranium from the ground. It's not like I own a uranium mine or anything, that's just from some stupid scraps of land that have been in the family for a couple of generations now. Any farmer or rancher owns far more.
Note that this is a problem of scale, not of know-how--any two-bit dictator can overcome it.
If you want cheaper, United Nuclear will sell you uranium, currently at $23/gm for very high purity. Buying a bomb's worth would no doubt set alarm bells ringing but if you used enough identities and did it slowly enough I would think you could get it without questions being asked.
Likewise, a cavatron is not that complex, I would think a decent engineer could build one. It's quite capable of producing weapons-grade material. Again, the problem is simply one of scale--cavatrons are slow and power hungry. Bomb-makers use things like gas centrifuges because they're cheaper and faster. (Note that a high purity source is not required although it will speed things up as the time and power requirements are based on the number of atoms you process.)
Thus it should be obvious that with sufficient money you can build a bomb, no specialized engineering needed. That means it's impossible to prevent them from being built.