Think of what happens when a rainbow forms: zillions of water droplets are scattered through the air refracting light. You see a rainbow because light from the sun is very directional and makes all the droplets refract light in the same way. Droplets located along a specific arc all scatter light of a given color at just the right angle to reach your eye. Droplets located along a parallel but slightly different arc do the same thing, but for a different color. The directionality of the light is the key to making that happen; if the light were soft and therefore coming from all directions, the droplets would scatter light in all directions and you'd never see the colors organized into bands.

You've got a very similar situation with the nail polish: there are thousands of tiny particles in the polish reflecting light, with some diffraction being caused either by the particles themselves or perhaps by the film of the nail polish. With a directional light, all the flakes forming a certain angle with the incident light and your eye will reflect the same color toward the viewer (or the camera). With a soft light, each flake will reflect light from many directions, and the result is a white or gray appearance.

You definitely need a directional component to make that iridescence show up. Experiment with the light or camera position to get the colors you want. You should also experiment to see if you can mix in a certain amount of softer light to make the skin of the hands look better without overwhelming the colors you want.