It will likely scare them the first time as it’s new/unfamiliar, but they’ll begin to normalize it with repeated events (as long as there is no physical/situational aggressiveness toward them). Once they acclimate to the singing, they might still get a small jump scare if you begin abruptly belting out something, but as you continue the song they would likely relax back down recognizing it as not a danger. I find most pets will try to hide/runaway when they don’t like a sound, so indifference from a pet is akin to general acceptance of your presence imo.
Here’s wishing you a wonderful performance!
Changing hair styles specifically for the car reminds me of some emergency responders who were talking about the horrific crash scenes where people wearing plastic hair claw clips that broke apart and become shrapnel or the clip simply lodging in the skull through blunt force contact (usually) with the headrest.