I would never consider a song composed by an English soldier serving in India about an Indian subject to be 'Indian' or Asian; similarly a song sung by English-Irish sailors or cotton screwers who happened to work temporarily in Mobile is not an "Alabama" song.
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I would agree, most folk songs, including work songs and the kind labeled chanteys, are sung in the styles of today. Except during the "rediscovery" period of the 1950s, their popularity did not extend to a general audience. The 'tearjerkers' of the 19th century either make us cringe or smile, but we no longer share their feeling.

Few of the songs of the early 20th century ( E. g., the volume Heart Songs, "Dear to the American People,") are heard today, let alone those of the mid-19th century.