Light has zero rest mass; that's not the same as it having zero mass. The mass of a photon can be derived from its energy using the good ol' E=mc2, and the photon's energy depends on its frequency.
Photons always travel at the speed of light, regardless of their frequency or how fast you move while observing them. Since momentum depends on mass and velocity, and the velocity of light is fixed, you can also derive the momentum of a photon from its frequency.
This means that to increase the total momentum of a laser, there are two things you can do: increase the frequency of the photons or add more photons.
You might still largely have to hand wave after that though, because the amount of energy you need to add to get any serious momentum from light is so high, the kinetic effects would be largely irrelevant.
For example, you say the output is a purple beam. So lets say you are blueshifting down to violet and then adding photons to increase momentum. Violet is 380-450nm, so say 400nm. That means each photon has an energy of 5×10−19J and a momentum of 1.7×10−27 kg m/s. For comparison, per wikipedia a 5.56 NATO cartridge has a momentum of 3.8 kg m/s. If you multiply out the number of photons to get 3.8 kg m/s of momentum, your laser's energy will be 1.1GJ, which wolframalpha helpfully tells me is equivalent to detonating a quarter of a ton of TNT.
As for Newton's third law, well momentum must be conserved. However much momentum you add to the laser is equivalent to the recoil you will feel when you fire the weapon. So in the above example, we have a laser gun with about as much recoil as a normal M-16 that hits like a decently sized bomb. If that sounds good, great.
If not, I recommend hand-waving more. Whether or not your magic device handwaves conservation of momentum depends on how much kinetic energy you want to impart in the target. If it's smallish, just accept it as recoil, otherwise handwave it.
Keep in mind that just because your laser doesn't have much momentum of its own doesn't mean it can't throw things around. Hitting something with a lot of laser energy will cause rapid ablation - parts of the surface will heat up so fast that they explode outward in one direction, which also pushes the object back in the other direction, away from the laser. You don't have to worry about the laser's momentum here because the momentum of the object comes from the equal and opposite momentum of the surface being blown off. This would be a case of the photon energy being converted into kinetic energy in the target.
