SJoy
I could be wrong but I believe that both the owner and the dog walker are responsible. The owner is the “principal” and the dog walker is the “agent” for the principal. If an agent acts on behalf of the principal (walking their dog) in a negligent manner, then the principal is liable as well as the agent. If you feel the need to take civil action, you would probably file suit against the principal which is the owner.
I would highly suggest that you do. If the owner is aware of the dogs tendancies to be aggressive and allows a dog walk to walk the dog, they are being negligent and just plain stupid. I have a bully breed and he can be aggressive. I would NEVER let anyone else walk him. We never walk him right by other dogs or even people. We know his limits and work within them so that everyone is safe and has an enjoyable walk.