Is there any chance that you'd do better with an HDMI switch whose output feeds an audio extractor?

Let's say chances are 2/3 that you can find a switch that works perfectly, and 2/3 that you can find an extractor that works perfectly. Finding a device with both parts working perfectly, in the same chassis, is less than 4/9 because of the number of unicorns involved in integrating the two parts flawlessly and making HDMI signals behave.

And, let's say you suddenly had problems with audio: you would not have to throw out your great switcher while searching for a replacement audio extractor.