If I connected both ground (black) wires to one pole of the switch would flipping the switch cause both devices (breadboard arduino and laser) to turn on? Or is there something I don't know about the power that this would cause an issue?
Actual you can switch a common ground from the two power sources with their grounds tied together then on to a single pole switch and then on to the arduino's ground and breadboard ground.
It's a little unusual to do it that way, but if you only have a single pole power switch (two terminals) and want both parts to power on and off together, it would work as you wish.
Using a double pole switch for each of the positive voltage sources is the more usual and better method, as if there was ever a DC current path for a device wired between both +3 and +9 sources there could be a discharge path through the two voltage sources. That is not a normal situation with most arduino projects using mixed voltages.