Controlling a Peltier module using PWM

like L293N for the Arduino

That won't work. The ancient L293 is extremely inefficient and can't come close to handling 3 Amperes. Consider a modern motor driver, like this one, keeping in mind that most motor drivers require more than 5 to 6V for motor power.

Using a direct voltage to drive them might destroy them.

Not if you use a low voltage power supply (say, 3.5V). Since you are cooling only, you can simply use a logic level MOSFET as a switch.