Yes, rank on shirts did not appear until the turn of the century, It seems to pop up first in the phillipines around 1899 or so. The army eventually had to authorize a smaller form of chevron, as the 1884 chevrons were simply too large to put on a shirt sleeve.
The army officialy exausted its stock of CW uniform items by 1880. It must be remembered that thanks to rather "shady" war contractors, a lot of those 4 button fatigues were child size! (Paid by number of outfits produced!) Within a few years the 4 button was gone, and by the late 1880s the uniform situation had much improved. After 1886 or so, it was rare to see troops in the field in other than issue gear, unlike the hardscrabble decade just after the wars end.
That was unifom items of course, accoutrements like belts, holsters, slings, canteens, mess gear, and sundry, lasted well into the 1930s! (Indeed, there is a rumour of some Navy NCO wearing such gear on his patrol boat in 2005!)