Cant fault you for trying. It been done before by bodyshops so you theres no reason why you might not drop lucky if you send the letter out to plenty of companies. I cant see why it would be such a bad idea if a bodyshop is not that busy or not working upto its capacity. it would only take one or two people to contact them after seeing the details on the car for them to benefit by it.

Of course, if the bodyshops your asking are fully booked up and working to maximum potential then they'd be no point really as they dont need or dont have time for extra work.