Analog audio (speakers) is an AC waveform, that's why your speakers move back and forth. If you just apply a DC voltage to a speaker it will move one way and stay there. The osillations in the voltage/current are what move the speaker. If you put a diode in-line with the speakers, then only one direction can flow to the speaker and it will no longer work.
How to make it work... I don't see a way to integrate it with the factory stereo.
Your only real options are a separate dedicated speaker, the integrated speaker in the CB, connecting it to an Aux-in jack on the radio (but then you'd have to change the radio to only hear the CB, and not the radio); or if you're really really crafty and feel like a project, research and design a electronic circuit that can do signal sensing and switch the input from the radio to the CB automatically (this is a Electrical Engineering mid/upper college level project).