Thank you, everyone, for your responses. I appreciate the time and thought you put into writing them. I decided to decline for the safety of the hamster AND the adult. I'm often told I am over-protective with pets and overthink everything, but I think in this case my first reaction to decline was appropriate. Your posts indicated similar thoughts on the matter and a few that I hadn't considered. Thank you.
Ria, in response to your comment, regarding a fish tank: There is a large fish tank there and four therapy pets living onsite along with therapy pets brought in by volunteers. They have enough therapy pets.