If he's preparing them for racing Abarth style I'd call him a race car tuner or custom car tuner and his business would be a race/custom car tuning shop.

abarth 500 preparato gare
https://www.google.es/search?q=È il più grande preparatore d...

race car tuner shop tuned fiat abarth 500
https://www.google.es/webhp?sourceid=chrome-instant&ion=1&es...

custom car tuner
https://www.google.es/webhp?sourceid=chrome-instant&ion=1&es...

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Note added at 3 hrs (2016-03-28 12:29:22 GMT)
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There are a few levels of performance tuning, starting with just go-faster mods such as spoilers and stickers, remapping modern engines or full engine and suspension mods. A road legal car might be souped up to fast road spec, whereas a race car will usually be a lot lower, lighter and have a more drastically tuned engine that may need rebuilding after every race.

fiat 500 elaborata
https://www.google.es/webhp?sourceid=chrome-instant&ion=1&es...

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Note added at 5 hrs (2016-03-28 14:32:45 GMT)
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Thanks for your comment Pamela, but if you took the time to check out some of the links I've posted you'll see people do indeed race Fiat 500s.
If this person is just restoring the car he would be a restoratore rather than a preparatore and the car would be restorata rather than elaborata.
One of the requirements of classic car registration in fact is that the car must be totally original so you shouldn't have different paint, engine, suspension or parts. It should be as it was when it rolled off the production line years ago.
If a car has been elaborata it will not be original spec but made to look or drive faster than stock by a tuner working out of his shop.