The article refers to Carlos with "her" in all cases.
https://www.discogs.com/release/1343533-Walter-Carlos-Switch...
The article refers to Carlos with "her" in all cases.
https://www.discogs.com/release/1343533-Walter-Carlos-Switch...
https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Gend...
To answer your question, she/her is correct, and a brief note that she went by Walter at the time is sufficient to avoid confusion.
She was living as a she at the time.
The first pressing of Switched on Bach didn't even have a name on it. She had to fight just to get W??? Carlos on the second pressing. (I have the first pressing framed.)
In hindsight, it might have been less confusing to just use W. Carlos as her professional name. I certainly was confused because, in 2000, my college textbooks said "Walter Carlos" but the record store had CDs by "Wendy Carlos." I didn't figure it out until I Googled "Walter Carlos."