Why would you have to do that? The package is already sat there, completed and in a warhead. You'd just have to find a way to remove it from that warhead and place it in another, and nuclear weapons engineers are pretty intelligent people when it comes to that sort of problem solving.
At its most basic level then sure, and as Rroff says the older stuff was far less protected than newer stuff.
Its always easier to reverse engineer than to first engineer, but even then there are risks.
What everyone was most worried about at the time was them falling into disrepair and into bad hands.
It happened to many ex soviet assets. I remember reading about someone visiting an ex USSR navy yard (not sure where now) and being able to go straight into a nuclear sub. At lot of their stuff was literally rotting away and some was finding its hand into bad hands as people were not getting paid.
People were most worried about the threat of the time, other states that would have been happy to use them as simple dirty bombs.