As far as I know, there is no built-in button to trigger all caches.
But it is possible to script that. You just need to keep the action out of the evaluation of the tree. One method would be to write a script that traverses the objects and activates the button whenever it encounters a Jiggle deformer.
Naturally, that script needs to be clicked on manually by the animator. So, you need to make sure that the animator has that script, and has it embedded in their layout.
The other method is to hide the script in a Python tag, but not in the Execute method but behind a button. You can then put that tag somewhere else where it would not be hidden from the animator, and it will find the jiggle deformer(s) by itself. The disadvantage here is that the animator must select the tag before they even see the cache button.
If you don’t want to script it (or have it programmed for you), you are probably best off by hiding the jiggle deformers in a separate layer (maybe in a layer hierarchy, depending on your animation concept) and tell the animator to make the jiggles visible if they want to cache. This would still allow for an uncluttered tree, since the jiggle visibility can be switched off.
(I admit I’m not so much a friend of hiding stuff in the OM with the layers though, since making a level in the tree folded and invisible prevents you from accessing any child objects.)