The answer is styptic powder. Milady describes it precisely: "Styptic powder or liquid, made from alum, is an antihemorrhagic with astringent properties that can stop the bleeding of small nicks or cuts." Every working barber recognizes this by sight — it's the classic tool reached for the moment a razor or clipper nicks skin.
Astringent, pH-balanced fresheners or toners, and plain alcohol — the other choices — are related skin-care products, but none of them is specifically classified as an antihemorrhagic (a substance that stops bleeding) the way styptic powder is. This connects directly to the "intact skin blocks pathogens" question above — once skin is broken, an antihemorrhagic like this becomes relevant.
Milady Standard Barbering, 6th ed., Ch. 13 (Men's Facial Shaving), p. 352: "Styptic powder or liquid, made from alum, is an antihemorrhagic with astringent properties that can stop the bleeding of small nicks or cuts."
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