After reading the lyrics of many versions of "The Red River Valley," I am beginning to change my mind as to the origin.
Most have many words and lines and a style in common, suggesting a common source in sheet music, songsheet or songbook.
Sentences, such as "And the love we exchanged 'mid the bowers" ('flowers' in some) and "Do not hasten to bid me adieu," "dark maiden's prayer," etc. suggest a parlor song.

The date attributed to Kerrigan's music seems a little late for many of the (anecdotal) reports, and the lack of preserved copies of the sheet music, leave doubt in my mind about that source. However, printing in one of the many 'song books' of the times would insure fairly widespread distribution of the song.
You also mention "Wehman's Collection of Songs" (no. 24). Even multiple sources?
Wehman Bros. issued song books and joke books, including Irish and minstrel. Delaney Pub. put out hymns and could well have issued many song books. These sem to be extermely rare, but many of the 19th c. songsters were used to disintegration. I found none in the Library of Congress index, but I may not have searched properly.