Find Yourself a micro controller of choice or even a 555 timer. Any 5v logic will do. Gather all other components listed above

Solder the 10K pull-up resistor to any free header pin. Lay the resistor  horizontally, to save space.

Mount the NPN transistor close to the resistor. Try to get the base lead of the transistor as close as possible to the unconnected side of the resistor. Bend the transistor on its side, to again save space. Solder them together.

Note: The resistor has to connect to a IO Pin, the emitter of the transistor has to connect to ground. I suggest making the connections correspond to ground and an IO pin on the Adruino that are next to each other. Example, GND and P 13

Connect the emitter lead of the transistor to a header pin.

Next, terminate the camera's shutter pin to the collector of the transistor. Connect the ground of the camera to the ground rail which is connected to the Arduino's ground, and the transistor's emitter.

Seal your connections with hot glue to protect them.