I had a similar problem at one time when I needed to switch between a local studio and the main studio, both coming in on composite STL's at the transmitter site. I used a low-power coaxial relay that could be remotely switched by applying 12 volts, and rigged a latching circuit that could be turned on by the remote control. Latching the relay "on" switched the local studio on line, normally off was the main studio feed. These little low power coax relays used to be common, but I just checked Surplus Sales and their selection seem very slim. Check some of the other amateur radio supply outfits--many are made with BNC in/out which makes hook-up simple.
Most modern processors will tolerate a little extra coax between the processor and exciter.