I understand the problem that you have, it is however possible to use an A/B switch.
But the best possibility indeed is to use the CD changer input on your radio. It is accessible, if you know the exact pin-out. It will work like an Aux input. However I found out today that it isn't that easy. Sometimes the radio uses a Digital Bus and then there is no option than an FM modulator. However the problem usually is the connector, I hope you'll be able to find that.