You DO need to disconnect both batteries when powering the circuit down.
There are a couple of options to consider.
1) Modify the circuit to run from a single-ended power supply. This is easy to do in your circuit because the only nodes that connect to ground are the 4- (+) inputs on the op-amps and the load.
The changes needed are simple: add a voltage divider reference from V+ to V- with the mid-point going to the 4- (+) inputs on the op-amps. Add a bypass capacitor across the lower resistor for stability.
You will also need to add an output coupling capacitor. The (+) side of the cap goes to the op-amp output pin, the (-) side goes to the load. I normally also add a bleeder resistor from the (-) side of the capacitor to ground (V-) so that you don't get a thump when connecting the load.
2) Use a DPST or DPDT switch to disconnect both batteries.
3) There is a simple trick that can work well under certain circumstances: connect the batteries in series with blocking diodes. You then use a SPST switch to short the diodes.
simulate this circuit – Schematic created using CircuitLab
The downside of this approach is that the ground terminal will bounce around by one diode drop as current consumption changes from (+) to (-). Depending on the PSRR rating of the op-amps, this can lead to distortion at the output.
However, I have successfully used this technique in the past.