Can exposure to radiation from laser hair removal of chin be a cause of thyroid cancer?

unlikely. Thyroid cancers are not rare. All lasers used on people have to be approved by the fda to be safe in regards to radiation exposure.
Doubtful. Cancer caused by radiation is a result of time and dose. Dose delivered by laser hair removal is probably small to cause thyroid cancer even over time. But, anything can happen. Be reasonable and sensible. Thanks.