Sorry. We can tell
Hypothetical science questions have a nasty habit of having answers.
If the particle changes position, its charge moves and the movement of charge has visible effects (eg magnetism). By contrast the ripple of communications from one charge bumping the next bumping the one after and so on can be measured moving from point A to point B. The former goes at walking speed, the latter at near the speed of light.
So both happen, and we can tell the difference.
Cheers,
Ben
"... I couldn't see how anyone could be educated by this self-propagating system in which people pass exams, teach others to pass exams, but nobody knows anything."
--Richard Feynman
