Neapolitan??

 In his 1911 book -- The Theory of Noble Art of Fencing -- Samu Chappon claimed to know Neapolitan fencing (foil + dagger). He said that this type of fencing is highly beneficial both for men and women, because it trains the left hand, develops the chest, and equally strengthens both hands. [2]

„Neapolitan” fencing (Fig. 15)

 We don't know for sure the origin of this peculiar way to use a dagger in icepick position. The most likely explanation is that this „Neapolitan” fencing was invented by Joseph Hartl, fencing master in Vienna, who taught stage fencing to actors. In 1884 Hartl and his female students visited Hungary at least twice and performed several fencing demonstrations in order to popularize female fencing. Chappon could see such a fencing display of foil skills, and later used it as a good marketing tool.

Hartl's pupils in 1885 [3]

 The true Neapolitan way of using a rapier and a parrying dagger can be studied in many historical sources (Texedo, Vega etc.).

Don Pedro Texedo Sicilia de Teruel (1678) [4]

Alvaro Guerra de la Vega (1681)

 In the Vega's picture we could see two fencing guards with a rapier and a dagger: Spanish (Postura Espanola) and Italian (Postura Italian??), with the parrying dagger in the left hand, and ahead of the tip of the rapier. Neither Texedo nor Vega depicted daggers held in icepick position.

 Another historical source -- Don Giuseppe d'Alessandro: Di spada. Con un trattato del modo di Curare I'infermita dei cavalli loro preservativi el altri notizie curca li medesmi. Antonio Muzio, Napoli, 1723.

Don Giuseppe d'Alessandro (1723)

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1. Third edition is available online at the MEK (Hungarian Electronic Library).
2. „A Napoly-vívás, mint a 15-ik ábra mutatja, úgy hölgyeknél mint uraknál, nemkülönben gyermekeknél igen jó testedzést idéz elő. A balkezet rendkívülileg erősbíti, a mellkast fejleszti s mindkét kezet egyformán erősíti.” [Page 76]
3. „The illustration was published in 1885 in the French, Le Journal Illustre. They are the famous women students of Maitre Hartl from Vienna. They traveled all over Europe and the United States giving demonstrations.”
4. It is a Spanish-Italian fencing treatise dedicated to the viceroy of Naples.