I am completely perplexed by your question. Not only is there not a character of "Choragus" in Shakespeare's Hamlet, but there isn't even a CHORUS in Hamlet. I am left wondering if you misspelled the word and mean the Choragos (the leader of the Chorus) in Greek Tragedy such as Oedipus Rex, or if you are under the influence of an incredibly advanced professor who wants you to project some Greek Tragedy ideas onto Shakespearean Tragedy. I will give you a short answer to both and hope that I have touched on what you are looking for.
In Greek Tragedy, the leader of the Chorus is called the Choragos. The Choragos occupied the most prominent position on the stage and was the most revered of characters, always giving good advice as the reasoning voice in the play. A good example of the altruistic Choragos is in Oedipus Rex where the Choragos is, of course, the true human reason of the play. The Choragos always urges Oedipus to see reason, to listen to the wise sage of Tiresias, to choose moderation over extreme, and to grasp truth.
Now we are left with Hamlet, and there is only one choice if you are looking for the voice of reason, the Choragos: Horatio. All of the other characters, both major and minor, have too many flaws: Hamlet (inaction), Claudius (ambition and lust), Gertrude (lust), Ophelia (insanity), Polonius (the fool), Rozencrantz and Guildenstern (spies), etc. We are left with the very honorable character of Horatio, always loyally at Hamlet's side and always able to give words of sage advice. It is Horatio who holds the dying Hamlet in his arms. At that moment, Hamlet says the following:
O good Horatio, what a wounded name,
Things standing thus unknown, shall live behind me!
If thou didst ever hold me in thy heart
Absent thee from felicity awhile,
And in this harsh world draw thy breath in pain,
To tell my story. . .
O, I die, Horatio
Note Hamlet's request here: "to tell my story." This is the biggest job of the Greek Chorus, and therefore a main goal of the Choragos! Horatio, who is the one character not left dying on the stage, will be alive to tell Hamlet's story. And, truly, Horatio believes it is a noble one. One of the most quoted thoughts of the play is spoken by the loyal Horatio:
Now cracks a noble heart. Good-night, sweet prince;
And flights of angels sing thee to thy rest.
This quotation bleeds spirituality, friendship, and truth. Among other things, it proves Horatio to be the true Choragos of Shakespeare's Hamlet.