For the work involved, I don't think a switch would help a lot. While the Electronic Climate Control System is sort of a set-and forget system, there are a lot of parts that would have to be installed in the conversion process. Sensors, wiring, dash control panel and the controller would best be taken from a donor car. The heater/A/C box under the dash would have to be swapped out as well. Figure on tearing out the entire dash of your car and swapping out a number of wire looms. Dont' know if the CCM does anything with the C68 option, but if it does, then a new CCM would be required.
Coupes with all of their glass surfaces absorb the suns rays and act like an oven. I would use the solid top instead of the see-thru top and have a dark as legally possible tint installed on the rear hatch. It looks like you already have that from the pic, but also a black car doesn't help either
Make sure the A/C system is working properly and get the cold air temps as low as possible as measured at the outlet vents. Your 96 probably uses R-134a as the refrigerant and it just plain does not cool as well as R-12. You might want to check with a reputable A/C shop to see if they can use a different refrigerant that will provide colder air temps.