Doing what you want to do is incredibly easy in Adobe Audition, which developed from Cool Edit Pro, so I wouldn't be surprised if they both worked the same way. If both channels are closely matched as to dB, I find that I don't need to worry about cross fading. If they are not closely matched, you might want to first take care of that with Cool Edit Pro.
Here is what I do with Audition:
1) Highlight a section of the music that includes the dropout and a little more for safety (zoom in if you want to replace very little more than the minimum necessary). You can highlight both channels at first.
2) Press the ^ or V arrow so that only the section from the good channel is highlighted.
3) Press Ctrl + C to copy the good channel
4) Press the ^ or V arrow so that only the channel including the dropout is highlighted.
5) Press delete to blank out the channel that has the dropout.
6) Press Ctrl + V to copy the section form the good channel to the channel with the dropout.
7) Play back the section you've repaired starting a few seconds before the repair to be sure you don't hear any glitches.
Doing it this way is not at all time consuming (unless you have a lot of dropouts to fix). It almost always works great for me, but as jerryfreak says you might run into some situations that don't sound right without adding cross fading. I always insure that the channels are a good match in dB's first and have so far not found it necessary to do that.