Can we say "Shabbat Shalom" on Shabbos

[Director Michael]

If the Noahide is greeting first, it's better for him or her to just say "Shalom!" so the Jew has the opportunity to respond "Amen!" (as the Talmud instructs) and then return the greeting.

If a Jew wishes a Noahide "Shabbat Shalom" or "Gutte Shabbos" by mistake, the Noahide can say "Thank you" (the polite response) and then "Enjoy your Sabbath!"