200 square feet could easily be cooled from existing system without much expense. I wouldn't add a duct but instead install a fan in a stud bay. 12x12 louver near floor inside adjoining room,fan with shutters near ceiling in sunroom. Switch fan on-off as needed. Unless you plan insulated glass for intire project,I'd at least use some on west end. Hinged doors or shutters on west side might be considered instead of insulated glass.