Tactical warhead yields are typically in the 10's or 100's of kilotons, not megatons as with strategic weapons.
The warheads on tactical nuclear missiles such as the now-retired US Air Force SRAM-A are surprisingly small. You could put one in a large duffel bag, although you probably couldn't get through airport security with it.
The rest of the system to enter the PAL codes or otherwise control the warhead are not very large and don't require a lot of electricity, either.