I know you mean well OP but you've gotten it all wrong. Natural essential oils contain some of the worst allergens in perfumery. Synthetics are safer. Currently, the EU severely limits the use of naturals and a handful of core aromachemicals in nearly always present in naturals must always be listed (geraniol, linalool...) because they are known irritants.
It sounds intuitively right that what we can eat must be wonderful on our skin but unfortunately it isn't so - citrus essential oils or innocuous-sounding things like cinnamon can be strongly allergenic. Perhaps the most irritating perfume component that is been phased out is oakmoss. You could collect that from oak trees and cook up your own perfume but it triggers a rash in some perfume wearers (I'm one of them). For this reason, there are industry regulations that are trying to make perfumes more synthetic - to make them safer.
If you find a natural perfume that lasts well (exluding some very heavy naturals like labdanum, castoreum and birch tar), you can be almost certain that synthetics that modify their volatility have added. Those synthetics are often synthetic musks that you can also find in your laundry detergent.
Perfumers do not like going all natural for the following reasons 1) health and safety issues limit the use of naturals 2) lack of longevity 3) the price of raw materials 4) a very limited palette - the use of synthetics moved us beyond citrus colognes and rose and jasmine perfumes.
A decent perfume line that claims to be natural, with a good perfumer involved, is Honore des Pres. Mandy Aftel works with naturals too. I've tried some of her perfumes and while I respect her efforts and vast knowledge, the perfumes last perhaps for thirty to sixty minutes on my skin. There is also a wonderful South African perfume maker, Frazer, her solid perfumes are lovely.
And sorry, nothing natural about Jo Malone and Lush.