Dalton,
it took a moment to look through some stored book boxes.
From Roster of Soldiers, Sailors, and Marines . . . Residing In Nebraska, June 1, 1893. ,Jacob North & Co.,Printers, Lincoln, Neb 1893
on page #399 in the New York section:
" Name Rank Company Address
Wisner, J. R. Private Unassigned 15 Hansen, Neb "
Not sure if this is your man, but I only checked in the New York section and this is the sole Wisner listed there. Curious about the unit ambiguity, and "15" is not identified as to branch.
(Something to keep in mind, in the latter part of the war numbers of the Heavy Artillery units were re-outfitted to act as Infantry and sent to the front to fill in losses caused by combat and the three-year enlistments coming to an end. No need to man the big fortress guns as the South was weakened, and these "Heavies" were large units, somewhere in the neighborhood of 1,200 to 1,500 men. They looked like a whole brigade at a time when the typical veteran Infantry regiment may have numbered 300 or less. You'd have to do some looking to see if you can find any history on the 10th NYHArty, or a 15th if one existed. Wouldn't make any difference as far as locating your man, but just to flesh out a possible background history.)
RCJ