Can I accept the 7 Laws without accepting Rabbinic authority?

This is a step in the right direction, because at some level you would be connecting with the 7 Noahide Commandments that are incumbent on you as one of the Children of Noah, but it is an incomplete acceptance. At this level, a person might still mistakenly transgress in some ways. A person who doesn’t learn the details of these commandments as they are elucidated in the traditional Torah sources is likely to err in his own (biased) judgment of what he assumes would be permitted or forbidden by G-d. Just as an example, one might naively (and wrongly) assume than if one commits euthanasia, it is not considered to be murder in G-d’s eyes.

On the other hand, if you observe the Noahide Code properly (which requires learning the correct explanations based on the Torah Law for Gentiles), you will be able to know and follow the righteous path. Even more so, to earn the ultimate reward that G-d will give to the “Pious Gentiles of the world” (Hasidei Umot Ha’Olom in Hebrew), it is necessary to also accept that the obligation to follow the Noahide Code comes from G-d’s commanding it through Moses at Mount Sinai, as 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] and Gentiles who wish to have eternal life need to connect with this “Tree of Life” in the proper way, through its 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.