Capt James R Kavanaugh is not the man you have in mind. According to the 1850 and 1860 census of Jackson Parish LA, he was born in Alabama about 1825. He organized a company called the "Jackson Grays" which entered Confederate service July 7, 1861, Camp Moore LA. It became Co "K", 9th Louisiana Regiment. After Colonel Richard Taylor was promoted, Kavanaugh was elected Major on Nov 20, 1861. He was sent home to recruit Feb 10, 1862, and happened to be in Huntsville AL when Federal forces captured the city, Apr 11, 1862. Imprisoned at Johnson's Island OH, Major Kavanaugh was exchanged for Major W A Caffey, 1st Kentucky (U S) Cavalry, and released at Vicksburg MS, Sept 20, 1862.

Kavanaugh no longer had a position with the 9th Louisiana and eventually became Enrolling Officer of Caldwell Parish LA. He was paroled at Monroe LA, June 9, 1865.

Unless you have a first name for the Cavanaugh/Kavanaugh brother who came to New Orleans, it will be difficult to identify one among so many. Do you have further information?