I would imagine that the wavelengths that caused the most damage would vary depending on the ingredient, just like how fragile the compounds are varies with a whole selection of other parameters.
The alcohol content clearly is at risk as much or more than the ingredients which are in solution in the alcohol, but that's more of an evaporation risk than a degradation one. As for each of the compounds, as chemicals they are all stable to a certain degree but again that varies from compound to compound.
For example, water is an extremely stable compound and if you were to bring together hydrogen gas and oxygen gas at room temperature and pressure, the merest hint of a spark and you would hear a large bang and suddenly have none of either and a large puddle of very hot water instead. The reaction of hydrogen and oxygen (both in gaseous form, both already in molecules) to make water is serious exothermic and the bonds within the water are so stable that getting it back to being just oxygen and hydrogen takes a huge amount of energy no matter how you try to achieve it. Some compounds are enormously stable and take huge energy input along with specific conditions to degrade them, whereas some will react with the gases in the air given half the chance.
I would guess (purely a guess at this point) that the most damaging wavelengths are going to be in the ultraviolet and infrared ranges, but that still covers quite a large range. Even if one wanted to find out the answer to this practically we could be here for the odd 20 years waiting for the answer with the thousands of different compounds which could be involved in a perfume.