You probably have got a situation, as you say, where lack of airflow in the cupboard is making stored items damp.
Some damp companies are quite happy to come to your house and go around stabbing at the walls with a meter. We went with a company whose proprietor preferred to investigate without one. A damp meter can give a reading indicating damp from virtually anything.
Sort the airflow to the cupboard, and if you have no obvious signs elsewhere of damp then I wouldn't do anything else.