Can you do the following tests?
Disconnect the dry contact switch from the sensor, and connect a multimeter across the two wires from the sensor.
First, read the open-circuit voltage that the sensor puts between the wires with the multimeter in the DC Volts mode. I'm guessing it will close to the 3V battery battery voltage.
Second, put the multimeter into the DC milliamps mode, and read the short-circuit current that the sensor puts through the multimeter. I'm guessing it will be a few tens to hundreds of uA.
Report back with the numbers, and I will devise a circuit that does not require external power...