Fernando,
There is a couple of ways to do this. One way is to use a 4066 switch like you suggested. (RS-232 almost never runs at the full spec of +-12V.)
Another way is to add additional serial ports to the PC. USB to RS232 converters are fairly cheap. It would be easy to add two of these devices. As long as the total number of COM ports is less than about 6, Windows does not have a problem.
Finally, you can still find some mechanical switch boxes that would do this. While your manual states that the should not be connected or disconnected with the PC running, this is not a real requirement. The radio should be able to handle any transients from such a connection or disconnection. I have "hot-plugged" hundreds of RS232 devices through the years and never had a failure. The techs at work do it all day long.