Can a Noahide rebuke and strongly and repeatedly persuade a non-Jew [a complete stranger] who is in the process of converting to Judaism, not to covert and rather remain a Noahide and keep the seven Noahide Laws because of their halacha obligation as mentioned in Melachim uMilchamot 8:10? I don't understand this because the Beit Din strongly discourages external factors like this that may interfere with anyone's conversion process or spiritual journey.
I don't know of any Noahide halacha about this type of situation. Even if there was, who's to stop him? The question seems to be asking for an opinion. "Can?" Yes, he can, in a free country.
The Noahide would need a legitimate and compelling reason to involve himself in someone else's conversion process. That's just not possible for a stranger.
If a Noahide met a total stranger, found out the stranger was in the process of conversion, I can think of no reason that would make it appropriate or acceptable for the Noahide to "rebuke and strongly and repeatedly persuade" the person to stop the process and just be a Noahide. It is none of their business and could cause emotional harm to the convert and their family.
Even if the Noahide assumed too much of a connection to the stranger he just met and thought good-natured teasing would increase camaraderie, he could be wrong. A sensitive person could take it seriously, and that changes the dynamic. Maybe he could do so with his Army buddy who after years, decided to 'take the leap.' This just isn't the type of thing to play around with a total stranger.
If the Noahide knows the convert, and has some reason to be concerned, or knows the convert is acting deceptively and feels compelled to 'do' something, he should talk with the rabbi. But really, even then, it's none of his business. It's between the person and the rabbi doing the conversion. Blowing the situation up with drama is not the way to go.
If it happened, and the convert told his rabbi, perhaps he would be advised to simply avoid the person and not engage with him? Or don't share with strangers he's still in the conversion process, just be a Jew in public and let it be? Seems best not to open oneself up to someone else's scrutiny if possible.