It is not possible to directly convert a liquid mixture from/to ppmw and ppmv units. Firstly, to clear up any uncertainty, I assume you are talking about a mixture of two liquid, and not one liquid plus a solid or gas. The reason for my statement is that doing this type of "conversion" implies that the liquid volumes are simply additive. For many liquid-liquid systems, this would NOT be a good assumption. Mixing water and ethanol, for example, is not ideal, and the volume of the resulting mixture is not the sum of the two liquid volumes.
To put some numbers together for the sake of illustration, let's say we mix 100 liters of pure ethanol with 100 liters of pure water and ended up with 195 liters of ethanol-water mixture. What is the volume fraction of ethanol? Would it be 100/195? If you think "yes", then is the volume fraction of water also 100/195?
HTH,
Doug