[mikatelyn]

My thoughts on this would also be "no".
1. As stated above, pet therapy typically includes holding/stroking the pet. A hamster tends to want to run around. If the person holding the hamster isn't used to it, they can easily drop the hamster, possibly injuring the hamster.
2. If said hamster is dropped or otherwise escapes, now you have a loose rodent in the hospital/care facility. As rodents can carry certain human illnesses, this is probably a liability for the hospital, and they probably wouldn't appreciate it. For the hamster, this has become life threatening if they cannot find a way back to you.
3. i understand that hamsters can get sick from certain human diseases. Perhaps not the best thing to expose them to a facility that carries a lot of disease.
4. Hamsters get scared from new smells and situations. They are creatures of habit. Exposing them to a bunch of new people in a new environment could very well get the patient you are trying to help bitten. If said patient is also immunocompromised (such as a chemotherapy patient or a poorly controlled diabetic), a small bite could turn into a big infection, which has now just exposed you to a lot of liability.
Now, granted, you appear to live in Canada and not the US, so maybe your risks with the medicolegal system are less dramatic, so take this last point with a grain of salt.

Pros:
1. Your patient might really enjoy the hamster
2. The hamster may enjoy a new experience if it is bored with its current environment, but I'm thinking this would be pretty iffy.

All in all, the cons outweigh the pros in my mind.

This might be different if the person meeting the hamster is coming to your home, and at reasonable hamster waking hours. Then you'd have to decide if you like/trust this person enough to give them that kind of personal information.