Assuming that the major as recorded by the university and appears on your transcript is “computer science” most employers won’t know or care about the differences in the CS degree given with the BA rather than the BS designation.
You’ll have time to take courses in departments other than the CS department. But in practice not a lot of time. CS requires a significant amount of coursework, some of it preparatory, some of it basic, some of it state-of-the-art. Pick a university or two that offers CS as a major, and review the course catalog. Taking care not to skip prerequisite courses in the sciences and math work through a thorough practice schedule. Make sure you cover data structures, operating systems, introductory hardware, some compilers, some internet, some database, some design formalism, etc. Make sure that most of the CS courses have a project component. Then ideally with a recent talented CS graduate look over the courses on your list. Keep the essential courses. Your future employers expect those. Keep in mind that your future employers also expect lots of As. Those required CS projects that are at the heart of many CS courses take a lot of time. What’s left? I expect time for a handful or two of courses that are the “plenty of electives”.