Nope, that won't work, you are switching power, not line level signals. What would work, is to use the line level outputs from your amp, feed it into the volume control unit you found, and hook up another amp for speakers B.
Not what you wanted to hear, I am sure. But, that B output is speaker power level, so you can't apply line level electronics to it. You could put a power resistor in series with each Speaker B, say 100W, 2 to 4 Ohm resistor, which will cut the volume a bit. It will also affect the sound quality and not in a good way.
Another option, which you probably don't want to hear, is using a set of speakers that are less sensitive than Speakers B.
If your main amp is a home theater receiver, you should be able to control the volume to Speaker B in the settings menu.
Not what you wanted to hear, I am sure. But, that B output is speaker power level, so you can't apply line level electronics to it. You could put a power resistor in series with each Speaker B, say 100W, 2 to 4 Ohm resistor, which will cut the volume a bit. It will also affect the sound quality and not in a good way.
Another option, which you probably don't want to hear, is using a set of speakers that are less sensitive than Speakers B.
If your main amp is a home theater receiver, you should be able to control the volume to Speaker B in the settings menu.