Final answer:
The production of skin pigments is not a function of the accessory structures of the integument but is performed by melanocytes within the skin itself.
Step-by-step explanation:
Among the options provided, the function of producing skin pigments is not a function performed by accessory structures of the integument but by cells within the skin itself.
The skin's melanocytes produce melanin, which gives the skin its color and offers protection against ultraviolet (UV) radiation.
So, the correct answer is E) production of skin pigments, which does not directly contribute to the protective function of accessory structures like hair, nails, and glands, which perform different roles such as protecting the skull, sensation of touch, thermoregulation, and excretion of sweat.