"Are Wax Melts Safe For My Pet?"
Wax Melts, much like any product containing fragrance can harm your pet - irrespective of wax type. The largest study of different waxes ever conducted recently found no real change in soot emissions between wax types. 
It is indeed the fragrance which can be harmful to your pooch or feline. Fragrances are made up of chemical compositions which contain natural ingredients such as Benzene, which has a sweet scent and is incredibly common in wax melts, but can cause respiratory problems in humans and pets alike.
The fragrance within wax melts can also contain a handful of a short list of allergens, which yourself or your pet may also be allergic to - the allergens can be easily found on the product packaging.
The above is true of any product containing fragrance - and you'd literally have to read the product contents to see what it can cause.
Moderation is encouraged with any fragranced product. For instance, wax melt manufacturer Nuscents have a cat at home and will eliminate particular scents from the home environment if they sense a change in him.