The word is actually σοφός (sophos). σοφῷ (sophō) is the dative form.
The Greek σοφός occurs over 20 times in the New Testament (Matthew, Luke, Romans, 1 Corinthians, Ephesians, 1 Timothy, James, Jude).
With respect to Romans 16:27, there is uncertainty whether verses 25-27 - the Doxology - were part of the "original form of the epistle" to begin with. Metzger comments here:
While recognizing the possibility that the doxology may not have been
part of the original form of the epistle, on the strength of
impressive manuscript evidence (𝔓61 א B C D 81 1739 itar, b, d*, o, vg
syrp copsa, eth Clement al) the Committee decided to include the
verses at their traditional place in the epistle, but enclosed within
By way of background, Metzger further explains:
A full discussion of the problems of the termination of the Epistle to
the Romans involves questions concerning the authenticity and
integrity of the last chapter (or of the last two chapters), including
the possibility that Paul may have made two copies of the Epistle, one
with and one without chap. 16 (chaps. 1–15 being sent to Rome and
chaps. 1–16 to Ephesus).
The doxology (“Now to him who is able to strengthen you … be glory for
evermore through Jesus Christ!”) varies in location; traditionally it
has been printed at the close of chap. 16 (as verses 25–27), but in
some witnesses it occurs at the close of chap. 14, and in another
witness (𝔓46) at the close of chap. 15. Moreover, several witnesses
have it at the close of both chap. 14 and chap. 16, and in others it
does not occur at all.
Scrivener's 1881 Textus Receptus (TR) reconstruction, the 27th Nestle-Aland "critical text" (CT), and the 1904 Patriarchal Text (PT) of the Eastern Orthodox Church all retain the same initial wording:
μόνῳ σοφῷ Θεῷ, διὰ Ἰησοῦ Χριστοῦ, ἡ δόξα εἰς τοὺς αἰῶνας. ἀμήν (TR)
μόνῳ σοφῷ Θεῷ διὰ Ἰησοῦ Χριστοῦ, ᾧ ἡ δόξα εἰς τοὺς αἰῶνας· ἀμήν (PT)
μόνῳ σοφῷ θεῷ, διὰ Ἰησοῦ Χριστοῦ, ᾧ ἡ δόξα εἰς τοὺς αἰῶνας , ἀμήν (CT)
The word σοφός is present in 1 Timothy 1:17 in the majority of manuscripts, as well as a 7th century revision of the Codex Sinaiaticus, a 6th or 7th century version of the Codex Bezae and about a half dozen other primary and secondary witnesses. The UBS editorial committee chose to exclude it from the Critical Text because it is omitted from all other versions of the Sinaiaticus, from the Vaticanus and about a half-dozen other witnesses. Scrivener's Textus Receptus and the Orthodox Patriarchal Text retained it.
With regard to your question about the original Greek manuscripts behind the Latin Vulgate, I don't think we know. The Douay-Rheims is translated from the Clementine Vulgate, which was published in 1592 - some 1200 years after Jerome published his translation out of the Greek.
* A Textual Commentary on the Greek New Testament (2d ed.), pp.476-77