Caution...
I would approach any detail shop with extreme caution. Far too few are staffed by skilled individuals. Basically the name of the game there is "buff n' go".
Similarly 99% of all body shops concentrate on "collision repairs", they have to in order to make money. The name of the game in those circumstances is "what will insurance allow", and many of the tech would not even think about how to 'disappear' a scratch.
There are shops that do RESTORATIONS where skilled detailers and auto body techs CAN make a good living by concentrating on on the things that most folks don't even know about, but they are few & far between. You probably don't want to pay hundreds of bucks for hours of work that really can't be justified on a 'regualr" vehicle...
I think that if the scratch is so minor that yoiu don't even think it went into the color coat you will have better results by researcing the technigues and DOING IT YOURSELF, if may take a few hours of reading up on the 'net, and maybe and hour or two of work & wait times, but it is probably the BEST way to handle this sort of problem (plus you can teach your two year a skill (in a decade or so) that will provide them with hours of amusement/possible income!!
