This question is usually asked in the context of manicure or pedicure where UV lights are used to quickly dry the skin. They are called nail lamps. These lamps produce UVA rays, on which Skin Cancer foundation officially says that these are in the bearable range. And bearable in this case means far lower to cause any adverse effect. Again, these are nail lamps and the effect is extremely minute to be considered as dangerous.
But the LED lights in your room, and book reading lights we are talking about, these lights, according to the research conducted by STONY BROOK University, do NOT harm your skin.
CFLs in comparison can cause harm to your skin, when these bulbs emit UVA and UVC radiations from the cracks in the phosphorus coating, according to another research conducted by Stony Brook New York and State University New York. CFLs are especially harmful when placed near to your skin, that is less than 25 cm, for a longer period.