Why not move said dog to another flight? If the handler has only one dog, shouldn't be much of an issue. I've seen last minute switches with a handler/judge where the judge had boarded one of the dogs on a truck, they moved ~5 dogs to another flight and had to move a couple back I guess, but the changes were done day one of the test since the HT Sec didn't know of the "conflict".
It's a single master flight.
HRCH Southern Breezes Black Cloud MH "Thunder"
HRCH War Eagles Midnight Storm MH "Boomer"
HRCH Southern Breezes Southern Bell MH "Bella"
HR Southern Points Cut To The Chase SH "Chase" RIP