Common Cathode Laser Diode - Photovoltaic photodiode
"Is there a circuit setup that will allow me to operate the photodiode
  in photovoltaic mode without voltage/current being supplied to the
  laser diode affecting it?'


You bet.







simulate this circuit &ndash; Schematic created using CircuitLab

But, of course, you'll probably have noticed that this isn't much different from your original circuit.