How long does it take an orange skin to decompose?

There is no definite answer to this question. It depends on the temperature, humidity, local species of microorganisms and insects (much "decomposition" is actually feeding by insects), and type of fruit skin.

Under the practically ideal conditions of my compost pile in summer, in less than a fortnight most fruit skins and vegetable peelings generally are no longer recognisable as different from soil, and may be totally gone.

People claim that orange peel takes about 6 months to break down in compost, due to the high concentration of anti-fungal oils. I don't know about that, as I've never tried to compost orange peel, but I can confirm that if kept dry, it lasts for years.