I have updated the schematic on my website to show the 1,000uF cap as a pair of 470uF electrolytic caps wired in a non-polarized manner. The 1,000uF cap must be non-polarized or you get a pop when switching.
This is a video to show what the mute switch looks like once constructed. Several folks have asked for help translating the diagram into the actual device. Thanks for all the positive feedback.