As to 'Shi (or Oi) no Okimi' in those historical books, there were no previous examples of ancient writers or editors using 'Shi (私)' for Manyogana (early Japanese syllabify composed of Chinese characters then used phonetically); so historians and other scholars would be able to conclude that the original writing was written in this way 'Oi no Okimi' and 'Shi (or Oi) no Okimi' was the transcription mistake.
これに関しては、「私」字を万葉仮名に用いた例が他に無いことから、本来「弘斐王（おいのおおきみ）」の誤りでろう。