Hi David,
I use the Hassy 110 on the Contax all the time.
The Contax Av metering is based on taking light readings at wide open aperture and adjusting its exposure time for the desired aperture that it can read from its lenses. With the Mam adapter, it cannot see your desired aperture on the Hassy 110. So, in order to get proper exposure, you must meter wide open, stop down and then manually set exposure. If you are only stopping down two stops or less, you do not have to switch to manual mode, but use the exposure compensation dial instead.
The exception to the above is when using TTL flash. The in-camera flash meter will stop down a Contax lens to the desired aperture, take a pre-flash at that aperture, and then set exposure accordingly. So, with the 110, you would first stop down to the desired aperture (and keep it there), trigger the pre-flash exposure, and then you are ready to shoot immediately. This will nail the flash exposure pretty much every time. As long as you do not close the pre-flash lever, the shutter speed will remain active in its memory so that you can re-use it until either you change aperture or the lighting changes where you must use the pre-flash meter again. The TTL pre-flash mechanism is one of the best and unique features of the Contax 645. It is both fast and accurate.
David