It should indeed be possible to achieve your desired goal with BITalino. On the back of the board you'll see several pins labeled Ox (x=1,2), in particular on the MCU block and on the side bars that have the plugs to which the sensors connect.
These are the digital output pins... you can toggle their state from the OpenSignals software by pressing the circles on the area labeled DIGITAL OUTPUT on the screen. You can also make a small tweak to the system to enable the state change to be controlled by the pushbutton.
To connect the digital output to the camera system you can either hardwire the GND and Ox pin of your choice to the camera input or (recommended), you can use an UC-E6 breakout cable to easily tap into to the pins:https://store.plux.info/cables/229-open-wires-cable.html
You'll see that the two UC-E6 plugs on the top right hand side of the Plugged main board expose the Ox digital outputs. With the breakout cable you have the pins that need to be connected to the camera system in individual wires.
As for the voltage, BITalino is near the limit... it should work, but it needs to be tested as the output on the digital pin changes between 0V and 3.3V. In case the Ox pin connected directly is not enough to trigger the camera system, just let us know.
The BITalino Team