I think you need to first define the word "right" in this context.
The Ramchal (Rabbi Moshe Chaim Luzzato) starts his famous work Mesilas Yesharim (The path of the 'Straight Ones') by stating that a person needs to clarify why he was created and what his purpose is in the world.
He answers by saying that we are created to enjoy a close relationship with G-d, which is the ultimate pleasure possible.
He then points out that once this is our goal, we then use it as a measuring stick for all of our activities.
We need to decide- is this bringing me closer to my goal of coming close to G-d, or making me more distant?
The mitzvos (commandments) are the way to build the relationship with G-d.
The rule in relationships is, the amount of expectations and obligations is proportional to the level of closeness to the relationship.
With your barber you have a minimal level of expectations- he cuts your hair the way you want, you pay him on time. That's really it.
With your friend, there's a lot more expected of you. Mutual help, respect, support, etc.
With your spouse you have even more responsibilities.
Your barber wouldn't be upset with you for not taking out the garbage. Probably your friend also wouldn't. But your spouse might. Why? These small acts are all part of the relationship of living with someone. Doing them builds the relationship, not doing them weakens the relationship.
This is a certain paradigm for the question of converting or not.
For any decent person, they can fulfill the seven Noahide laws and have a relationship with G-d.
It won't be anything nearly as close as a relationship built upon 613 commandments. That's a lot more intense, requiring tremendous sensitivity and significant attention to detail. it's very hard to live up to the standards of that relationship.
So when you ask yourself what is "right" regarding converting or not, the question can be rephrased: Do I think I can handle the intense obligations which come from such a close relationship?
Am I ready to get "married" or is it better for me to remain a faithful friend?
No one will force you into "marriage" and for many non-jews it makes sense to stay friends.
So in this regard there is no "objective right or wrong answer."
(By the way, this is really a life principle.
From a Jewish perspective, is it "right" to become an accountant?
There is no answer "yes" or "no" which is true for everyone.
It will depend on each person's aptitude, skill set, environment, alternative professional options, etc.
Yet Judaism will definitely say that for some people it is the "right thing to do" i.e. those people who will benefit from the steady job and will be able to contribute their skills to helping others.
And it will be "wrong" for other people- like a person who would be better off teaching a classroom and instead is stuck working as a CPA behind a desk, with their pedagogy skills languishing.
Right and wrong are not fixed, yet there is still a right or wrong answer to every question and every possible action.
The same is true over here- you are not obligated by the Torah, yet the Torah principles will still dictate what is right or wrong to do, and you are supposed to do what's right.)
One other perspective (another aspect of the above):
The question is asked how could Sodom have received such tremendous punishment for their wickedness if the Torah had not been given? How could they have known that they were so bad and immoral if the Torah defines morality and it wasn't given yet?
I saw an answer years ago in the name of the Ramban (Nachmanides- but I don't know where he writes it) that people have an intellect which is capable of deciding the proper course of action.
You don't need prophecy to know that stealing and sexual immorality is wrong. people are held accountable for not using proper common sense and for not arriving at correct intellectual conclusions even though they are not obligated in the Torah.
The basic principles of "right and wrong" can be derived from clear thinking, and this the intellectual basis for the Noahide laws. This is why they are binding upon all people, even those who have no access to the written Torah.
It's the basic code of morality, which means being the kind of person who has some connection with G-d (in a "friend" way, as mentioned above. There's a minimal level of connection.)
Via the Revelation at Mount Sinai and through learning and fulfilling the Torah, a person can become not just "moral" but "Holy"- there's the concept of kedusha.
This is what the commandments are for, and this creates that intense "marriage" relationship with G-d which is possible only through becoming Jewish.
(In fact, the term for marriage in Judaism is "kidushin"- a wife becomes "sanctified" to her husband.)
So the basic level of "moral right and wrong" can be obtained even without the Torah. But the "holiness right and wrong" requires the Torah.
