I wouldn't suggest making it damp, you want to keep the duckling warm and dry. If it is staying damp in there it might get chilled or sick. What kind of wood chips are you currently using? Cedar can cause a lot of issued so pine is recommended. I'm not sure it is the cat carrier that would cause the issues, if it's secure and warm with plenty of ventilation and room to get away from the heat if it is too much then I don't see the issue with it.