Do millimetre wave body scanners at airports produce radiation and is there any danger?

Difficult to answer: Scanners do produce electromagnetic radiation but it is non-ionizing. Ionizing radiation like x-rays are dangerous to DNA. Regard the millimetre wave radiation radiation likely it does not cause DNA damage to your tissue. There are some studies that show DNA damage outside of the cell but not really inside of the cell per say. Basically your ok for the very short time your in the scanners.