Shalom! If one is in the final stages of conversion to Orthodox Judaism, is not a Noahide, does not belong to any religion, is it appropriate for him to say he is Jewish? He does not want to tell strangers about his conversion.
Self-evidently, someone in the final stages of conversion to Orthodox Judaism is not yet a Jew. The Gemoro Shabbos 55a states that
חותמו של הקדוש ברוך הוא אמת
the seal of the Holy One Blessed be He is truth.
This potential convert wants to come under the tabernacle of HKB”H and in the process wishes to utter untruths. No he must not utter untruths.