The only way to permanently remove it, leaving it like new, is the sand, clean, and finish job. A fair amount of work and if you are that concerned with results, I'd let a professional shop do it. But why bother with this much work for a scratch? Wood furniture will eventually get scratched. There's just no avoiding it. Accept it, polish it, and smoke a cigar.

Polishing compounds are your best and easiest bet to hide the scratch.