The answer is a styptic, or antihemorrhagic, product. It constricts blood vessels to stop minor bleeding fast.
Astringents and toners just tighten pores — they don't stop bleeding the way a styptic product does. An emollient is a moisturizing ingredient, not a bleeding remedy at all. Any barber doing facial shaves should keep a styptic product within reach for exactly this situation.
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