According to some DSMers, you can use a one-wire oxygen sensor on your car instead of the four-wire OEM version. However, there may be some restrictions on their use.
Stock DSM oxygen sensors include a heating element that allows them to heat up to operating temperature faster, especially in cold weather. It is almost certain that a large number of owners have oxygen sensors with broken heaters. They don't notice the lack because the heater is not essential for O2 sensor operation. At worst, the oxygen sensor will take some additional time to heat up to operating temperature, and gas mileage might drop a little bit. So two of the four wires on the O2 sensor may certainly be considered optional, especially for those living in warmer climates.
The one wire on the non-DSM sensor is the oxygen sensor signal. Since there is no ground wire, the sensor must use the mounting point as ground. There is a small possiblity that this point might not be a good ground on some cars. Cars with upgraded downpipes might be suspect, as there is a grounding strap on the OEM downpipe that is frequently removed during the upgrade. This may affect the ground reference of the oxygen sensor to some extent.
Even in the worst-case scenario, this is highly unlikely to affect the operation of a stock or near-stock DSM. The precise reading of the oxygen sensor is not important, and is not used by the engine computer, so the ECU will not 'see' any shift in ground potential on the single-wire O2 sensor.
Owners of upgraded cars who use the O2 sensor for tuning purposes might have to be a little more careful. In many cases, owners rely on their oxygen sensors providing a consistent (if not accurate) reading. A shift of 0.100V might be enough to make their tuning more difficult. Thus, individuals who switch to a 1-wire sensor may have to spend some time re-learning their tuning methods to compensate for any differences in the new setup.
It must be noted, however, that tuning by OEM oxygen sensor is quite possibly the worst method of tuning a DSM. Owners with upgraded cars will hopefully have better and more reliable methods than relying on their O2 sensor.