It is the leaves that give off the ‘fumes’. Eucalyptus and other mrytles like as ti-trees, contain lots of small glands in their leaves that produce volatile oils. These oils have an insecticidal effect and help protect the leaves from a number of would-be pests. Crushing a leaf breaks open some of the glands, releasing the oils that you can then smell. These oils naturally evaporate from the leaves and in warm weather, the amount of evaporated oil is sufficient to produce a blue haze over eucalypt forests viewed from a distance. That’s how the Blue Mountains got their name.
Given the myriad of native animals living in eucalypt trees with these ‘fumes’ on an all-day, everyday basis, I don’t think they qualify as ‘dangerous’ when emitted from leaves. The distilled, purified oil is another ball game altogether. A number of birds use green leaves in their nests. It is thought it helps to reduce ectoparasites and may contribute to humidity. If it doesn’t harm hatchling birds surrounded by the stuff, I don’t see why it should hurt reptiles living in a similar environment.
There is also no problem with the bark per se. It is only if there are loose pieces which may cause a snake to fall if they give way - highly unlikely anyway.