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.
Using Linux with obscure hardware (CNC mills, chromatographs, etc) is a bit like punching yourself in the nuts, but still free.