You can make 'em big and healthy. But you still have the maintenance issues. Leaving one shuttle through the US transportation system would probably cause a fizzle yield. (There's something to be said for a national transportation infrastructre that's right at its operating limits.)
How possible is it to shield those from satellite sensors? Copter, drone sensors? Sensors on harbor cranes?
Shielding a nuke means hiding both the gamma emission (which means a fair amount of lead) and the neutrons (which means lots of lightweight material, like resin or styrofoam.
Unless it's very carefully done, the weight distribution of the shielding might call attention to it.