Will deleting this data affect my campaign save-game or fastest lap times at all, or will it simply just remove the ghost ship that goes around during speed laps and time trails?

Can't see why it would affect your save. Unless you're very tight for space you might as well keep them though - they're only small files and they'll end up getting remade by the game anyway when you try a speed lap or time trial.

I'm pretty sure there's a thing in Options that allows you to just turn off the ghost if you really dislike it that much.

I find the ghosts help with the record keeping. if you beat your ghost then you have a new record.

I agree they help you to keep track of how your doing
and yes there is a thing in options to turn them off