NK has a working ICBM with a nuclear warhead today. It's already done. The time to stop it was back in the 90s.
AFAICT we know they have blown up stationary nukes and shot out inert ballistic missiles.
Lets put miniaturization aside and focus on another aspects, which i judge will be more critical.
The warhead must survive mechanical stress of launch and reentry, and thermal stress at reentry. The question is: can it be designed only with computers and public knowledge? They could build small hypersonic wind tunnel to collect data and simulate the rest.