I found a bit more - realized Aaron was right age for Civil War so took a look
U.S. Civil War Soldier Records and Profiles about Aaron Welch Name: Aaron Welch Residence: Sylvester, Wisconsin Enlistment Date: 21 Jan 1865 Rank at enlistment: Private State Served: Wisconsin Survived the War?: Yes Service Record: Enlisted in Company A, Wisconsin 46th Infantry Regiment on 21 Jan 1865. Mustered out on 27 Sep 1865 at Nashville, TN. Sources: Roster of Wisconsin Volunteers: War of the Rebellion
Civil War Pension Index: General Index to Pension Files, 1861-1934 about Aaron Welch Name: Aaron State Filed: Nebraska Widow: Sarah J Welch Roll Number: T288_505
It says: Welch, Aaron Service - A 46 Wis. Inf. Widow - Welch, Sarah J. Date of filing - 1896 Nov 20 Nebraska
I sent for two of my ancestor's Civil War pension files and there was much more info included than I had expected so you might want to think of doing that for Aaron.
Both of the files I sent for had a lot, including several affidavits from family members, and one had marriage records for the fellows three wives and names of all the children born to them. They also include death info for them as the widows needed that info to collect the pension after their husbands died.