I don't see how possible, though. Two humans, one managing their dog which probably takes both hands and the other managing the aggressive dog doesn't leave much opening to fiddle with cell phone, tap camera from lock screen, scroll over from still to video, begin recording, yada yada.
Back when everyone started to audition for the Instagram Squad we had some people showing up with regular looking shooting glasses that could record video. Maybe a cheap pair of those on amazon. I think the pair I saw was just a single button tap to start/stop recording video. Probably easier to keep a pair of those handy and throw them on when you first see the dog. Then you can focus on the task at hand and manage the video later.
Something like these: https://www.amazon.com/s?k=video+gla...f=nb_sb_noss_2
I have no idea what's what in terms of product quality. But any one of them is probably better than trying to grab cell phone video.