Should be quite easy to remove any WiFi/cellular/satellite antennas from the car’s computer. (Might be trace/chip antennas, so make sure to get those). If you’re extra paranoid, get the GPS antenna too, so it can’t simply record data indefinitely.
Might take a few hours to go through the car to make sure you get everything, but you won’t be limited to super old cars.
Does your car lock up outside of cell coverage? I’m not suggesting removing the radios themselves, just the antennas. To the car, it will just always be out of range.
The antenna used for talking to the keys might cause trouble, but those are either inherently short range inductive systems or are receivable using a 20$ RTL SDR to verify it’s not sending anything else.