No nuclear-capable nation is going to raise their hand and volunteer to destroy their weapons. Since no one is going to go first, no one is going to follow suit. All we can hope to do is stop any other nations from acquiring nuclear weapons. Using nuclear energy may be alright, but that shouldn't lead to manufacturing weapons.
The creation of nuclear weapons was a revolutionary advance in human technology, and humans are very reluctant to give up on their technology. It is highly unlikely that nuclear weapons will ever be done away with. Plus, the possession of nuclear weapons is a sort of insurance policy for many countries.
As much as I would like to say yes, it is unlikely that nuclear weapons will ever be destroyed. They are too dangerous and powerful and nobody is going to volunteer to do it first as it makes their country immediately vulnerable. The weapons have too much mental and physical weight to be destroyed.
If anything, nuclear weapons have kept countries away from going to war. They know how much devastation there would be if many were ever used against citizens at the same time. However, the countries that have nuclear weapons are able to exert a lot of power over countries that don't have them. Nobody wants to give up that power.