Both readings have early manuscript support
The reading μυστήριον (mystery) finds early support in P46vid? א* A C 88 436 itr, 61 syrp copbo Hippolytus Ambrosiaster Ephraem Ambrose Pelagius Augustine Antiochus.1 UBS3 cites P46vid? in support of μυστήριον however the question mark follows "vid" because the editors were not sure of the reading in P46. Phillip Comfort however confirm the reading as mystery based upon the the fact that the broken letter eta is visible prior to the final four letters (ριον) hence UBS4 and NA28 both now read P46vid in their respective apparatus2.
The reading μαρτύριον (testimony) is well supported in early manuscripts (אc B D G P Ψ 33 81 614 1739 Byz itd, g vg syrh copsa arm eth Origen al)3
The earliest text we have P46 supports "mystery" as do other early and diverse manuscripts, however the same can be said for the variant reading "testimony" The evidence is inconclusive.
Possibility of textual emendation
Competent textual critics such as Zunts and Fee have argued that μυστήριον (mystery) is a scribal emendation influenced by 1 Cor 2:7 "ἀλλὰ λαλοῦμεν θεοῦ σοφίαν ἐν μυστηρίῳ τὴν ἀποκεκρυμμένην, ἣν προώρισεν ὁ θεὸς πρὸ τῶν αἰώνων εἰς δόξαν ἡμῶν"
Fee (1987: 88 n. 1) for example questions why a scribe would substitute the less expected and less colourful “testimony” for the more familiar “mystery” (as do also Robertson and Plummer 1914: 30; Barrett 1968: 62–63; Wolff 1996: 47).
Zuntz (1953: 101) also argues that if Paul had used “mystery” here, it would cause it to “lose much of its force” in 2:7. He thinks that a scribe changed it to “mystery” to assimilate it to 2:7. I am not convinced that Zuntz makes a good point here - it is hard to understand how using mystery here would cause it loose force in 2:7.
Other scholars such as Brown and Metzger have argued that μαρτύριον (testimony) is a scribal emendation based upon 1 Cor 1:6 "καθὼς τὸ μαρτύριον τοῦ Χριστοῦ ἐβεβαιώθη ἐν ὑμῖν."4.
One explanation for the substitution of μαρτύριον (testimony) is the rise of mystery religions, Thiselton (2000, 207) suggests that scribes may have made the emendation to avoid misunderstanding.
Again the evidence is inclusive as there are some good arguments and good scholars on both sides.
The harder reading
The word “mystery” occurs twenty other times in the Pauline corpus. The phrase “mystery of God” occurs twice (1 Cor. 4:1; Col. 2:2), while the word “testimony” occurs only five times. The phrase “testimony of God” never appears, only “the testimony of Christ” (1 Cor. 1:6) or “of our Lord” (2 Tim. 1:8). This would make “testimony” the harder reading5
The harder reading seems to favour μαρτύριον (testimony) over μυστήριον (mystery)
It seems that one can draw upon the context of 1 Cor 1-2 to find support for either reading (see above).
The passage is focusing upon Paul's mission which was to testify only of Christ, who is the mystery of God. However the immediate context seems to favour mystery. Chapter 2 focuses on the need to receive revelation from the spirit of God to understand the riches of God that are in Christ Jesus.
In each unit so far, Paul employs a word that he will emphasize in the
next unit. Proclaiming “the mystery of God” also would not have been
inappropriate as the subject of his first preaching, particularly in a
synagogue setting. It makes the best sense in the context. The content
of the mystery of God is spelled out in the next verse: “Jesus Christ
crucified” (2:2).Garland, D. E. (2003). 1 Corinthians (p. 88). Grand Rapids, MI: Baker Academic.
The internal and external evidence for the genuine reading is divided. The textual evidence in inconclusive and whilst the harder reading would probably be "testimony" the context suggests "mystery" as the preferred reading. This difficulty is reflected in the division of scholars and is displayed in the text of most modern English versions of the Bible. Most follow testimony (KJV, NKJV, RSV, ESV, NASB, NIV, TNIV, NEB, HCSB, NET) many of those same versions provide a margin note of "Mystery" (NKJV, RSV, ESV, NASB, NIV, TNIV, NEB, HCSB, NET).
1 Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (p. 480). London; New York: United Bible Societies.
2 Philip W Comfort, Tyndale (2008) New Testament Text and Translation commentary.
3 Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies\’ Greek New Testament (4th rev. ed.) (p. 480). London; New York: United Bible Societies.
4 Philip W Comfort, Tyndale (2008) New Testament Text and Translation commentary.
5 Garland, D. E. (2003). 1 Corinthians (p. 88). Grand Rapids, MI: Baker Academic.