Can I accept the 7 Laws without Orthodox Rabbinic authority?

That would certainly be a first step in the right direction. You would be connecting with the 7 Commandments that are incumbent on you as one of the Children of Noah. But it would be an incomplete connection and acceptance. At this level, a person might still mistakenly transgress in some ways.

Without learning the details of these commandments as explained by traditional Torah sources, a person is likely to err. Everyone has his own (biased) judgment of what he assumes would be permitted or forbidden by G-d. For example, one might naively (and wrongly) assume that euthanasia is not judged by G-d as murder.

On the other hand, if you learn these commandments properly, you’ll be able to know and follow the righteous path. This requires learning the correct explanations based on the Torah law for Gentiles. Even more, with correct observance, one can earn the reward that G-d will give to “Pious Gentiles of the world”. (In Hebrew, these are the Hasidei Umot Ha’Olom.) For this, one must accept that the obligation to follow the 7 commandments comes from G-d’s commanding them through Moses. That happened at Mount Sinai, so it is part of the eternal Divine Truth of the Torah of Moses.

This obligation includes the details of the Noahide Code as they are found in the Written Torah and the Oral Torah. The Torah is G-d’s “Tree of Life” [Proverbs 3:18]. Gentiles can connect with this “Tree of Life” through the Torah- based Noahide Code.

The details of the Noahide Code are provided in the book The Divine Code: The Guide to Observing the Noahide Code, Revealed from Mount Sinai in the Torah of Moses, by Rabbi Moshe Weiner of Jerusalem.