This is pedantic but you're thinking of "romanization", the act of transliterating Japanese with the Roman alphabet (romaji). There are different systems of romanization, most notably Hepburn and Kunrei. In Hepburn shi is correct, in Kunrei si is correct.
It sounds like you're saying "si" are not valid characters in the Roman alphabet.
Ok yea I see what you’re getting at — my terminology was overly narrow. By “romaji” I specially meant “romanization I’ve chosen for this article”. I do offer an explicit note that other romanizations exist, but outside of that note, I tried to stay within a single self-consistent system, so this nuance was lost.