The manufacturer's recommended fuels in order of cleanliness (completeness of vaporization):
White gas > Kerosene > Unleaded gasoline > Diesel
Now, white gas is a type of naphtha fuel, so I doubt that VM and P naphtha would harm your stove since the components are designed to handle exposure to white gas.
All naphtha is is a mixture of the more volitile petroleum hydrocarbons. All of the substances on the above list contain the hydrocarbons found in naphtha. As you work from left to right, they become increasingly "contaminated" with the less volitile (oilier) hydrocarbons. This is what causes residue build-up when using the "dirtier" fuels.
There are other possible (industrial, corrosive, etc.) contaminants that could be present in VM and P naphtha.
There is a crude and simple test that can be done to get a pretty good idea of whether or not these contaminants are present: Take a low, wide glass dish and IN A WELL-VENTILATED AREA (Read: Outside) pour about an ounce of the VM and P naphtha into it. Allow it to evaporate completely. If there is a oily residue it should still be fine to use in your stove. If the residue is gritty (crystalline) at all I would avoid its use in a whisperlite as this implies a potentially corrosive contaminant. If there's no residue at all (I suspect this will be the outcome) then it's equivalent in purity to white gas.