The two larger devices with the White Wires are the sounders. They are not speakers. They are Piezo Sounders. They are driven by a high voltage with very little current. Not sure if the driver circuit on the DS7000 can take a disconnected sounder set.
Anyway the White Wires from the PC Board are the ones. The White Wires between the two sounders just connects then together.
Sounds like you have a single pole switch with one set of contacts. Break one of the two White Wires from the PC Board to the sounder set. Connect the White from the board to one switch contact and a wire from the other switch contact to where you removed the original wire.
Note Piezo sounders maybe touchy to heat from a soldering iron. Cutting the White wire in the center maybe better than trying to solder to the sounder.