The requirements of one fulfilling the 7 commandant's of Noach is clearly mentioned in the Rambam laws of kings towards the end, that one must accept them because Hashem commanded Moshe at mount sinai, that Noach was earlier commanded regarding them, and the Rambam adds that if one merely fulfills them because one logically understands them etc then they are not considered one of the "chasidei umos haolam", rather, just like one of the "wise" amongst the nations, and another version says that they are not even considered as part of the "wise" amongst the nations
So if this person doesn't believe in Noach that means it wouldn't be possible in this current situation for him to accept the 7 mitzvos because Moshe was commanded at mount sinai that Noach was earlier commanded regarding them
This is also assuming he believes in Moshe and mount sinai in general, if not then based on the language of the Rambam, and I personally don't know of anyone who explicitly argues, then seemingly I can't think of any way, according to the text itself, that he would be considered amongst the "chassidei umos haolam"
Rambam hilchos melachim last halacha of chapter 8:
י
משֶׁה רַבֵּנוּ לֹא הִנְחִיל הַתּוֹרָה וְהַמִּצְוֹת אֶלָּא לְיִשְׂרָאֵל. שֶׁנֶּאֱמַר (דברים לג, ד) "מוֹרָשָׁה קְהִלַּת יַעֲקֹב". וּלְכָל הָרוֹצֶה לְהִתְגַּיֵּר מִשְּׁאָר הָאֻמּוֹת. שֶׁנֶּאֱמַר (במדבר טו, טו) "כָּכֶם כַּגֵּר". אֲבָל מִי שֶׁלֹּא רָצָה אֵין כּוֹפִין אוֹתוֹ לְקַבֵּל תּוֹרָה וּמִצְוֹת. וְכֵן צִוָּה משֶׁה רַבֵּנוּ מִפִּי הַגְּבוּרָה לָכֹף אֶת כָּל בָּאֵי הָעוֹלָם לְקַבֵּל מִצְוֹת שֶׁנִּצְטַוּוּ בְּנֵי נֹחַ. וְכָל מִי שֶׁלֹּא יְקַבֵּל יֵהָרֵג. וְהַמְקַבֵּל אוֹתָם הוּא הַנִּקְרָא גֵּר תּוֹשָׁב בְּכָל מָקוֹם. וְצָרִיךְ לְקַבֵּל עָלָיו בִּפְנֵי שְׁלֹשָׁה חֲבֵרִים. וְכָל הַמְקַבֵּל עָלָיו לָמוּל וְעָבְרוּ עָלָיו שְׁנֵים עָשָׂר חֹדֶשׁ וְלֹא מָל הֲרֵי זֶה כְּמִן הָאֻמּוֹת:
11
Anyone who accepts upon himself the fulfillment of these seven mitzvot and is precise in their observance is considered one of 'the pious among the gentiles' and will merit a share in the world to come.
This applies only when he accepts them and fulfills them because the Holy One, blessed be He, commanded them in the Torah and informed us through Moses, our teacher, that Noah's descendants had been commanded to fulfill them previously.
However, if he fulfills them out of intellectual conviction, he is not a resident alien, nor of 'the pious among the gentiles,' nor of their wise men.
יא
כָּל הַמְקַבֵּל שֶׁבַע מִצְוֹת וְנִזְהָר לַעֲשׂוֹתָן הֲרֵי זֶה מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם. וְיֵשׁ לוֹ חֵלֶק לָעוֹלָם הַבָּא. וְהוּא שֶׁיְּקַבֵּל אוֹתָן וְיַעֲשֶׂה אוֹתָן מִפְּנֵי שֶׁצִּוָּה בָּהֶן הַקָּדוֹשׁ בָּרוּךְ הוּא בַּתּוֹרָה וְהוֹדִיעָנוּ עַל יְדֵי משֶׁה רַבֵּנוּ שֶׁבְּנֵי נֹחַ מִקֹּדֶם נִצְטַוּוּ בָּהֶן. אֲבָל אִם עֲשָׂאָן מִפְּנֵי הֶכְרֵעַ הַדַּעַת אֵין זֶה גֵּר תּוֹשָׁב וְאֵינוֹ מֵחֲסִידֵי אֻמּוֹת הָעוֹלָם וְלֹא מֵחַכְמֵיהֶם