Sometimes people overlook the simplest things...

The Kzer-Za didn't even exterminate the DNYARRI, they enslaved them, and you're wondering why they didn't exterminate a race with insignificantly weak psychic powers in comparison - they have never affected one Kzer-Za (on Kzer-Za ships, there is only one Kzer-Za present, the captain, and the Syreen Song never affects the captain of the ship, therefore the Syreen Song has never worked on a Kzer-Za).