You are indeed not correct, paws are distinctly different from hands and the muzzle is a specific part of an animal's face.

Paws are different from hands in that they're made up ONLY of fingers, the equivalent to our wrist is way above the paw as part of the leg.

And the muzzle (also called snout) is the jaws+nose, the bit on e.g. a dog that sticks out in front of the face. It doesn't include things like the eyes.

Nah, paws are specific types of appendages. Monkeys have hands. But it's possible that back when the idiom was coined, it was different bc of that kind of logic.

Nah, raccoons def have little tiny hands.

Animals have faces, the muzzle is the snout (nose and jaw structure)

Humans are animals