I'm not too worried about loose nukes or nuclear terrorism. Every major nuclear power other than China incorporates PALs [1] into the design of their nuclear weapons. Without a centrally generated & authenticated code, they don't function. The PAL is designed such that disabling it requires dismantling the nuclear weapon, which means you need to have the know-how to build nukes in the first place to re-enable it.
This, incidentally, is why Ukraine gave Russia back its nukes after the fall of the Soviet Union. Without the codes in Moscow's possession they were just radioactive waste.
I do expect a number of smaller conventional conflicts to break out in the transition, because that's what always happens when a hegemon loses its monopoly on physical force. It's going to be a bloody few decades, but not the end of humanity.
[1] https://en.wikipedia.org/wiki/Permissive_Action_Link