Swords to Plowshares

According to wikipedia, there are 23335 nuclear weapons in existence. This is enough to sterilize the entire surface of the Earth several times over. These bombs are typically made of highly enriched uranium, with various mechanisms to set off the runaway chain-reaction that becomes nuclear meltdown.
However, uranium also has a peaceful use as nuclear reactor fuel. In addition, there is a way to use it for space flight at remarkable speeds, allowing robotic-probe colonization of the galaxy. For the first, the bomb must be dismantled, and its fuel carried to the reactor. U-235, the "fuel" of most of these bombs, is warm with radioactivity. Thankfully, it is the weakest, alpha, type. Alpha radiation is stopped by your skin, but the safety-concious can wear gloves to eliminate the risk. The daring are urged not to place it in their mouths. Newer bombs use Plutonium, which is warmer but still only an alpha emitter. Both these materials are a grey metal, and not glowing green as depicted in cartoons. Uranium is dull grey, like iron, Plutonium is shiny grey, like silver.
If we seek the reactor solution, we would take the bombs apart, ship the fuel to the reactors, and generate electricity for commercial use with them. This would have a problem of increasing the amount of spent nuclear fuel in the environment, which I will cover in a later essay.
If we seek the space propulsion solution, we need to construct very large ships, get them safely into orbit, find interesting destinations for them, and send enough equipment to do something useful upon their arrival. This would be expensive, but probably worthwhile. (Second home in case of doom of the earth, for instance.)
If we do nothing, then we have all these nuclear weapons sitting around. While most of them are too heavy to steal, there is always the chance that the host nation will sell the weapon, or elect someone insane enough to attack with them.