Thanks, y'all...not quite the answer I'd hoped for:
Misu - Saving a User copy of a style with all the mixer volumes at zero or the channel turned off doesn't work. Next time you open the style you are back where you started.
DerekA and iulistil2 - I'm aware I can do this in a registration for a song (I give every song a registration so I can have 8 different variations in the banks...sometimes I'm playing with a bassist, sometimes just a drummer, sometimes to a MIDI backing track etc) I'd hoped I could save a style so I can use it in a song without having to make up a registration first.
I guess no luck seeking a solution that's per style, not per song.