I did some testing on the small wires. Testing shows that the small wires do not carry power. They are used to close the circuit. I verified this by removing the wire from the main board and jumpering the pins. When powering up the amp with the wires removed and the pins jumpered, the amp powers up normally. However, the push button on/off switch only works to power on the amp. Just like when I was using the relay on the main wires, the amp would not shut off. Once the amp is on, pushing the power button has no effect.
I am still thinking that a DPST relay will work. This way I can use a single trigger to control both the mains power and break continuity of the small wires.