I am not saying it is the very best thing you can do, but it is something that will help at least some.
I always put two of these in my boat for winter storage and it keeps the humidity low enough that I do not have mildew problems. Different companies make similar products for closets etc.
MDR Damp Away Dehumidifier 12 Oz. MDR-300
Regular Price: $9.88
Special Price: $5.93
Marine Development (MDR) Damp Away Dehumidifier 12 Oz. MDR-300
Odorless. Automatically removes moisture from boat for months. Absorbs moisture from air and deposits it right into container. Place in cabins, lockers, closets, head, cabinets and other enclosed areas where moisture collects. Will absorb 250 cubic feet of moisture at 75% humidity. Lasts for months. Will not overflow. Perfect for winter lay-up.
Size 1 lb.
They also come in bag form:
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Damp Rid Hanging Closet Fresheners, 3-Count Package
None will do the job of a dehumidifier but they will remove some humidity from the air.