*well-made nuclear warheads

Pure fission bombs (the simplest kind of nukes) are literally just “let’s put enough of this plutonium close enough together that the chain reaction is sustained” a very simple warhead could have plutonium spaced just slightly farther than necessary for the reaction to happen and hold them that distance apart with a breakable or crumple-able beam so when the shell hits basically anything, the beam buckles, the plutonium moves closer together reaching critical mass, and adios

Could this still act as a warhead if you added propulsion (and prayed to the void the plutonium doesn’t break/vibrate free during acceleration) ? Yes. Would it almost certainly go off if it was dropped during a juggling act? Also probably yes.

Depends on the type of warhead. Implosion warheads are extremely finicky to get to explode, and damage to one could mean it’s never going to go off without significant repair. A shotgun type of warhead could theoretically go off if the two halves were sufficiently jostled together. Granted, the fact that this is a risk means they’re generally made with this in mind, and very sturdy materials are there the keep them in place until detonation time…

So yeah, juggling any nuclear warhead is probably extremely safe.

In fact, dropping them or shaking them up actually increases their yield.

Source: a can of soda.