I believe handkerchiefs existed as early as the 12th or 13th century, but not for nose-blowing. Hygiene being what is was, privileged fair damsels found their teeth often gone to rot by their early twenties and capable of generating a bit of a stench in close quarters. (Peasants, with their plainer, healthier diets, often kept good teeth much longer.)
The handkerchiefs were drenched in scent and held before the mouth while conversing closely, to spare their admiring young studs from keeling over from the stink.
Men's coat sleeve buttons, of course, came about as a direct 18th century reaction to Frederick the Great's guards wiping or blowing their noses on their uniform sleeves. Fred ordered buttons to be attached to thwart the wipers.