I've never used a Peltier, but...
Normally, you don't use PWM for heating/cooling because nothing heats-up or cools down that fast (except maybe a LASER diode 
).
You've probably noticed how the heater in your house works... It turns-on full-blast 'till it gets to the target temperature, then it shuts-off. Your refrigerator works the same way, cycling on & off.
There is usually some hysteresis. That is, a heater doesn't turn on until you are slightly below the target temperature, then it stays-on 'till you are slightly above the target. (That's so your heater doesn't cycle on & off several times per second.) You may not need to do that, but there's probably not any harm in slightly over-cooling your LASER.
I will also have to use an inductor or an RC low pass filter to smooth the signal before passing it to the Peltier for better operation.
You wouldn't want to do that either. The "R" would have to be small in value (for low voltage drop) but physically big to dissipate the heat, and that means your "C" has to be big, and the thermal-mass will automatically "smooth" the temperature change anyway.