You can. It is recommended to take your car to a reputable automotive repair establishment when you’d like it repaired or serviced. This is a possibility you could consider when you are familiar with a reliable car repair shop. You can check your local auto board for information on whether you have access to mechanics or garages to fix your vehicle.
It is possible to have your car assessed by an auto mechanic from home in case of the middle of an emergency. It is possible that they would prefer having it at their shop, but they’ll have access to all the instruments and tools they might require there. You may need to have your car tow to the garage.
You can easily find Corvette parts on the internet. Be sure to look around and be sure to do your research before committing to anything, in order to be sure you’re not ripped off.