Something like "Band of Brothers" by Stephen E. Ambrose?
I'm not aware of any collection of oral histories written after the fact, which is what Ambrose did with BoB (combined with his usual fast-food "history"). Side-note: I know you didn't mean anything by it, but on this sub, and anywhere else you're around trained historians, "Ambrose" is not a name you want to throw around all that much. The man and his family's assembly line school of "history" (yes, I keep using quotes on purpose because it barely qualifies as that) are not at all respected.
Sorry...just hearing the man's name gets me off on tangents. If you're interested in getting a primary source that has an outsider's perspective on the Civil War, check out 'The Freemantle Diary' by Arthur J. Freemantle. He was a British observer that toured both the north and south during the Civil War, and his reflections are fascinating! Although not specific to individual units, his observations do provide you a peek into what the war looked like on the ground.