Can the red battery cable be replaced/repaired without replacing the whole top part of the battery box?

Depends on how badly it is corroded, are you having starting or charging problems ? If the corrosion gets bad enough (and it will continue to get worse) it will eventually give you problems like vehicle not starting and or alternator not charging. Most of the time the corrosion is limited to the posts on the battery and where it connects on the engine block (negative cable blk) and starter (red positive cable). If this is where it is corroded you can easily clean them yourself with a "battery terminal Tool" cleaner or a wire brush/sand paper. I know these older vdubs 92 and older the cables do need to be replaced if they are still original, I've owned 5 MK2 golf/Jetta's and every one of them I had to replace the cables. Again tho this is a judgment call on what they look like I can't tell you yes change them nor can I say no there fine just clean them, you have to know what your looking at and determine what needs to be done based on what I have told you here, hope that helps.