I would not hire a mobile mechanic only because I want to drive the car to the mechanic shop have him look at it while it's at operating temperature and then drive it back to the owner. You can give the owner your license and insurance. They can take a picture of it and tell them exactly what you are doing. That you will be back as soon as the mechanic is done with his inspection.

Plus, you telling the owner exactly what you're going to do creates an opportunity for them to back out or be hesitant which will tell you everything that you need to know about that car.