My grandfather, who killed more animals than I can count, never killed anything bigger than a chicken with a blade.
He even shot the frikin minks he raised.
“Killing anything with a blade is not humane. I know this to be fact.’
Your facts are incorrect. Done properly the animal feels a slight pain when the knife cuts into its throat and then goes to sleep as it bleeds to death. The knife must be very sharp and the person must know what they are doing.
A .22 would be faster and less messy.
An even better option would have been to not breed the dogs and put yourself in a position where you had to kill them all.