You are probably overthinking the risks here.
Do what the professionals do. Just leave the car unlocked with the keys hidden somewhere inside, or tucked behind one of the sun visors. Or if you there are valuables inside the car and you want to lock it (unlikely, since you are leaving it for somebody else to use) then lock the car and hide the key in a front wheel arch, on the suspension.
The point is, if your car is parked in its usual place at your house, nobody who knows the area is going to assume it can be stolen. If an opportunistic thief can't see anything that is obviously of value inside, they aren't going to waste any time on it. If a professional car thief wants to steal it, the fact that it is locked is no deterrent at all. If they want it badly enough, they will turn up looking like vehicle recovery service employees and take it away in broad daylight, with all your neighbours watching and nobody suspecting a thing!
IMO you are taking a far bigger risk granting the use of your car to strangers for a long period of time, than the risk that somebody will steal it during the short transfer period.