Your man of mystery is Apollos, who also wrote the book of Hebrews. Apollos is the only reasonable answer to this question, in my opinion, based on internal evidence alone.
1 Corinthians 4:6 And these things, brethren, I have in a figure transferred to myself and to Apollos for your sakes; that ye might learn in us not to think of men above that which is written, that no one of you be puffed up for one against another.
Except for Paul, none of the Apostles (not even Peter, whom Paul mentions along with himself and Apollos in 1 Corinthians 1:12 and 3:22, but totally ignores in this later passage) attains to the stature of Apollos as an existential threat to the Jewish establishment in every city.
Paul was the pedigreed Pharisee, but Apollos was the "eloquent" orator that was "mighty in the scriptures" (Acts 18:24), a qualification that his letter to the Hebrews bears witness to. Apollos was a dangerous man.
Acts 18:25-28 This man was instructed in the way of the Lord; and being fervent in the spirit, he spake and taught diligently the things of the Lord...and when he was come, helped them much which had believed through grace: for he mightily convinced the Jews, and that publicly, shewing by the scriptures that Jesus was Christ.
In Corinth they were a team: Paul planted, Apollos watered (1 Corinthians 1:6), but beyond that it's evident that Apollos avoided sharing in Paul's persecutions, and preferred to travel incognito. As I see it, Paul's description of the brother "whose praise is in the gospel throughout all the churches" fits Apollos better than any other figure in the early church.