Disk Jockey with a "k" was long the standard American English usage.
For example, in 1951 Time Magazine, which would have been positively anal about using American English, had an article which on, "Critical tastes of U.S. disk jockeys, as reported by The Billboard last week..."
When CD's came along the creators used "disc" with a "c" and that spelling began to overtake "disk" when used for DJ's. "Disc" had also long been used in England for DJ's and when club DJ's started proliferating, the British "disc jockey" seemed to gain favor of "disk jockey" with that new trend. Most DJ's used to call themselves "jocks" or if they were trying to impress future in-laws they said they were "radio announcers" or "in broadcasting." Being a "disk jockey" sort of implied that you were not yet ready for a grown-up job. And I think it was Larry Lujack who once said, "The worst thing to be at a party is an unemployed disk jockey."