I found several references to PADDY'S WEDDING on the Internet:

Early American Secular Music and Its European Sources, 1589-1839 lists "Tid Re I, or Paddy's Wedding" as appearing in a collection called "Martial Music," published in Albany, NY, in 1807.

Click here quotes An Irishman in the Iron Brigade: The Civil War Memoirs of James P. Sullivan, Sergt. Company K, 6th Wisconsin Volunteers, Fordham University Press, 1993 – as saying that "Paddy's Wedding" was played at Gettysburg.

PADDY'S WEDDING was recorded by Dan Kelly in 1894, Peter Dawson in 1929.

There is an archived radio program containing the Dan Kelly recording on this page.