Yes, like Graham says, registrations are designed for exactly this - fast changes in live playing.
You can - and many do - have a whole bank of favorite voice combinations sitting ready to change at a single touch. If you do this, get a piece of masking tape and stick it on the keyboard next to the registration buttons with what is in each registration written on the masking tape. That way you don’t even have to remember.
As a bigger point, styles are seldom something you need to change on the fly. Typically you set the style between songs, so there is always plenty of time. But voices, like you say, often need to be changed in the fly.
There are many discussions about how to use registrations, but something to consider is to select your style via a play list using song names. Remember that styles can all be changed easily to some extent, on the fly anyway, using variation buttons. And leave the voice registration bank up ‘all the time’ for voice changes on the fly, and as the mood takes you.
Mike