Not really. You’re right they didn’t have the launch codes, but they had the material.

Nukes are easy, the hard expensive part is refining all the material. Once you have the material it’s literally just some regular high explosive, in some special shapes that are relatively well understood, and detonation timing. Even without being able to reverse engineer the existing devices, any country with a functional economy would have the resources to figure it out.

There’s a reason we judge countries nuclear pursuits based on enrichment amounts, it’s the only part that matters.