Coconut is not a nut in the same way a peanut is - but peanuts are not nuts anyway in the biological sense, just to confuse things. Coconut, sago palm and date palm are all in the same biological family, but not related to peanuts.
However, it is likely that due to the manufacturing processes, you may find warnings on labels that factories used to process the coconut also handle peanut products and other nut items, so you have to be aware of cross contamination.
There is a rise in coconut allergy as a seperate issue to peanut allergy, and an allergy to peanuts may laed to an allergy to tree nuts - which may lead to a coconut allergy.
Best advice is do not use the dessicated coconut in the recipe. Add a diced fruit to substitute the coconut - don't use an almond oil etc for the same allergy reasons of course - and bump up the amount of cornflakes perhaps to create a more crispy effect.