I haven't used screen protectors for the last four years and haven't had any issues with scratches. Then again I put my phone in a pocket with nothing else, and I don't do anything in a harsh environment. Your mileage may vary.
Unfortunately you probably won't find anyone here who still have that 12 year old device, especially because most members are from the USA which was never a large market for Sony devices. Your best option would be to try at XDA Developers forums.