every country today that desires a N-bomb has access to the science and means to build one (or more). It wasn't the same back then. Don't cloud the discussions with what we know now!
North Korea can't even feed itself. It's industry is backward. But it was able to build bombs. Supposedly Russian technologists were hired (like the Germans the US hired after WWII for the space program) to build rockets. Supposedly also North Korea exported some technology to Pakistan (funded by Quadaffi for an "islamic bomb") so it could match India.
So, you are probably right. Even a place like Zimbabwe could get a bomb if it were willing to pay enough (and able to). There is just too much black market technology and technical expertise around to prevent it.
It is noteworthy though that Iran does not yet have a bomb although it is certainly motivated. But Israel is so worried it is assassinating Iranian scientists and sabotaging Iranian facilities. ("Israel will not be the first to introduce nuclear weapons into the Middle East. Nor will it be the second." They have six German-built submarines which are capable of launching nuclear payloads.)
I read somewhere that if it wanted to, Japan (a space power) could get a bomb in "a month". The same is probably true of South Korea. I don't know how long it would take for Persian Gulf states, but it isn't inconceivable.
The trouble with all of this is that it increases the margin for error. The "super duper missile" Trump touted is supersonic and maneuverable. It's development by Russia and China (which motivated the Pentagon) is a direct response to American anti-missile technology (which is a direct response to places like North Korea). Every "advance" like this makes it more imperative to "launch on warning" so your "assets" aren't lost in a first strike. That, like space-based systems, is highly "destabilizing".
There is a book called "The Dead Hand", about a Soviet facility to detect incoming missiles and launch automatically. Apparently Breshnev still wanted some control. There was a hero in charge who, when the system malfunctioned and gave a false alarm, told Moscow that it was a glitch (even though he wasn't sure) and prevented a catastrophe.
Quite apart from who is and who is not an asshole (and I tend to think there are a lot of them), this is one reason to maintain dialogue even in the face of a "pissing match" with someone like Kim Jong-un. All sides have to have confidence that war is not an option, in my humble opinion. Swagger has no place in this arena, just firmness, dialogue, and respect for the vital interests of all sides. Who cares if they spit at you. Talk is cheap. This is an area in which we need grown-ups.