You can go into the warcraft keybinds, and unbind the keys that are associated with the pet bar.

Not sure how many actions you require for your pet.
I generally want:
- Pet Attack
- Pet Passive
And rarely:
- Pet Aggressive

They don't have to be on Control 1, Control 8 and Control 10.
And even if they are, you don't need Control 2-7 or Control 9 to be keybound.