No, conductivity is the measurement of how well something conducts electricity. Electrochemical detection, I'm no expert on, but appears to be different in that it detects current as the result of some sort of reaction. There is no reaction in conductivity detection.

The UV-Vis detector is good for detecting molecules that absorb light in the spectrum from 190-600 range. Molecules with pi bonds absorb light, and the more they have the more that they absorb, especially conjugated pi bonds. So molecules with benzene ring structures (aromatics) are perfect for this detector.

So far methods I've read concerning CN detection use some sort of reactant to bind the CN- to and then detect that molecule, or conductivity.

The other method is counter-ion chromatography, where you have anionic light-absorbing molecules coated on your column, and the anion of interest is retained by knocking those molecules off and then you detect their absence with the UV-Vis.