Is there a way to make the RESET pin work in the inverse?
My personal preference would be to attach a NOT gate to the RESET pin.  This can be constructed very simply from a single NPN transistor (or N-channel MOSFET) and a resistor.



simulate this circuit &ndash; Schematic created using CircuitLab
With the wire disconnected R1 turns on Q1 which pulls the RESET pin LOW.  With the wire connected Q1 is turned off, allowing RESET to be pulled back up by the pullup resistor that's built into the Arduino.
This method also won't interfere with the programming reset action of the Arduino.