My guess is that, unless you can find other letters describing the skirmish, you will not be able to identify the soldier wounded or the exact date he became a casualty. This late in the war, the regiment may not have been keeping up with its muster rolls and other paperwork or those records have been lost. Because most of the info in the compiled service records comes from muster rolls, I would be surprised if the CSR would be helpful.

Depending upon how diligent you want to be, there are two groups of records that you could go through in hope of finding your answer. One would be the Louisiana Confederate pension files. Finding the info here would depend upon the soldier surviving until the 1890s, filing for a pension, and mentioning his wound on the application. A second set of records would be almost as difficult to research. In the 1870s, Louisiana began giving land grants to wounded or disabled veterans. The Louisiana State Archives has these papers on microfilm and has produced an index that would allow you to search for anyone from the 1st Cavalry who applied.