Can I use a transistor as a switch to close a pin to GND?
Yes you can do it with a BC548 (or another NPN transistor). You need a circuit like the following one:




At the input of the circuit (i/p) you have to connect the arduino
output. 
At the output of the circuit (o/p) you have to connect the camera pin (SHUTTER or FOCUS).


To calculate Rc and Rb we need to check the Collector-Emitter Saturation Voltage in the BC548 datasheet. It is 0.25V for Ic = 10 mA, Ib = 0.5 mA. Low enough for your application. Then:


Rc = (Vcc - Vce) / Ic = (5V-0.25V) / 0.01A = 475Ω --> 470Ω is the closest E24 value.
Rb = (Vin - Vbe) / Ib = (5V-0.7V) / 0.0005A = 8.6kΩ --> This is the maximum value to have the transistor saturated, so I would pick a lower value to be on the safe side. I would recommend a resistor between 1kΩ to 4.7kΩ.


With this configuration, when you output HIGH from the arduino pin, you saturate the transistor and therefore the output goes LOW. So outputting HIGH from the arduino pin, you will trigger the FOCUS or SHUTTER signals.