Personally, when it comes to O2 sensors on Japanese car, it will have to be NGK or Denso.
The purpose of the Secondary O2 sensor is to monitor CAT's efficiency. Therefore, it doesn't daily driving as such. However, it is a MOT requirement item. So by it not functioning, you are no different from driving without MOT. (Obviously, no one will go up to your car to check unless you book it in for MOT. But still...)
Just be extra careful (not get involve in accident) you should be fine. Or should it happen, blame it on the accident itself.