I really think that this is not as big a deal as you think. The vast majority of schools don’t admit by major anyway, so whichever you put first won’t matter. For example, Harvard doesn’t admit by concentration and you can change your concentration freely, so what you put is unlikely to matter.
At schools where CS has competitive admissions you may want to apply to CS, because it’ll probably be easier to add a biochem major than to add a CS major. So if you are applying to any schools that have CS as a competitive entrance major, then you may just want to specify CS.
This is really also very unlikely to matter, and definitely not a red flag.