The person called cautious may have information that everyone else has mistaken for anxiety.

The person labelled cautious may simply be the one with information. They have seen this fail before, or know something about the equipment, the person, or the conditions, and their hesitation is being read as temperament rather than as evidence. Anxiety and knowledge look identical from outside.

So ask what they know rather than reassuring them. The question takes ten seconds and occasionally saves a great deal. And if you are the cautious one, lead with the specific reason rather than the feeling, since a stated fact gets considered and a stated worry gets managed.