A frightened pet should not become entertainment for people who know there is no danger.

An animal that is genuinely frightened cannot be told the situation is safe. It has no access to the joke, the context, or the fact that everyone watching knows nothing bad will happen. Laughter around a scared creature also teaches the people present that fear is funny when the frightened party cannot object. Amusement is not worth much weighed against real distress.

If an animal is scared, take it out of the situation rather than reassuring it where it stands. Say you would rather not film it, without making a speech, and change the subject.