Lets speculate a little bit for argument sake. Take this with a grain of salt because I am not a specialist, just a information hoarder.

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.

They might ask Russia for help