I don’t think he can because the RNC already happened making him the party’s nomination. The DNC hasn’t happened yet so the Democrats were able to switch candidates before they meet to nominate.
https://ballotpedia.org/ State laws and party rules on replacing a presidential nominee, 2024
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!