Video of what's being talked about
here. A Pikachu with 4 moves, Slam and 3 Electric moves, has an accessible Z-Move button. The Z-Move button seems to be pressed, and then the other moves fade out while there's an extended upper button, only it says "Hyper Sprint Attack das German" instead of "Slam".
Which makes me think that (these ideas not being novel), if you press the Z-Move button while holding the Normal Z-Crystal, one of three things could happen: only formerly damaging Normal-types attacks will be illuminated with Hyper Sprint Attack always showing in their place; or all formerly damaging Normal Attacks will display a corresponding replacement based upon their move type, Attack stat-using, Special Attack-stat using, or status move; or, finally, all Normal type attacks will display a replacement based upon move type, even status moves.
There is a 4th option (and this is the only other idea that's original at this point, the others have all been discussed), and it's a crazy one, and it's that all Normal moves like "Tackle", "Slam", or "Body Slam" have their own associated "slamming" Z-Move while "Slash" and "Cut" have their own "slashing" Z-Move. This could be exclusive to the other options, such that "Sing", "Growl", and "Hyper Voice" could have a common "soundful" Z-Move, despite including as a category both attacking and status moves, or else you could separate "soundful" status moves and soundful attacking moves, or even differentiate even further between special and physical soundful attacking moves.