The spray here isn't the kind that Westerners would think of as an antiperspirant — a (usually scented) deodorant with perspiration-inhibiting chemicals — but an "instant ice" spray. In the West, they're primarily used as sports medicine or first aid supplies, to treat injured muscles, but they're marketed as personal cooling products in Japan. Strictly speaking, you're supposed to spray a cloth or handkerchief and then apply that; direct application to the skin can cause frostbite.