There's no such word. ᾠδή - ōdē and ᾄδω - adō means noun:Song and verb:to sing.
Psalm means song of praise with or without instrument but it's etymology is from vigration of instruments, so mainly with instrument chords.
BIB Ephesians 5:19: “λαλοῦντες (speaking) ἑαυτοῖς (to each other) [ἐν] (in) ψαλμοῖς (psalms) καὶ (and) ὕμνοις (hymns) καὶ (and) ᾠδαῖς (songs) πνευματικαῖς (spiritual), ᾄδοντες (singing) καὶ (and) ψάλλοντες (making melody) τῇ (in the) καρδίᾳ (heart) ὑμῶν (of you) τῷ (to the) Κυρίῳ (Lord),”
BDAG3 reference on psallo: to sing of praise.
ψάλλω fut. ψαλῶ (Aeschyl.+; ins, LXX; TestAbr A 20 p. 103, 26f [Stone p. 54]; TestJob 14:2, 4; Jos., Ant. 11, 67; 12, 349; Just.; Mel., P. 80, 588; Did.) in our lit., in accordance w. OT usage, to sing songs of praise, with or without instrumental accompaniment, sing, sing praise w. dat. of the one for whom the praise is intended τῷ ὀνόματί σου ψαλῶ Ro 15:9 (Ps 17:50). ψαλλῶ σοι B 6:16 (Ps 107:4). τῷ κυρίῳ Eph 5:19: in this pass. a second dat. is added τῇ καρδίᾳ ὑμῶν in or with your hearts; here ψ. is found with ᾂδω (as Ps 26:6; 32:3; 56:8), and the question arises whether a contrast betw. the two words is intended. The original mng. of ψ. was ‘pluck’, ‘play’ (a stringed instrument); this persisted at least to the time of Lucian (cp. Par. 17). In the LXX ψ. freq. means ‘sing’, whether to the accompaniment of an instrument (Ps 32:2, 97:5 al.) or not, as is usually the case (Ps 7:18; 9:12; 107:4 al.). This focus on singing continued until ψ. in Mod. Gk. means ‘sing’ exclusively; cp. ψάλτης=singer, chanter, w. no ref. to instrumental accompaniment
Etymology of "a capella" reveals this Latin Italian word itself doesn't exclude instrument accompaniment.
1868, earlier alla capella (1824), from Italian, "in the style of Church music, in the manner of the chapel," literally "according to the chapel," from cappella "chapel" (see chapel). Originally in reference to older church music (pre-1600) which was written for unaccompanied voices; applied 20c. to unaccompanied vocal music generally. Italian a is from Latin ad "to, toward; for; according to" (see ad-); alla is a la "to the." Sometimes in the Latin form a capella.
Also denoting "that instruments are to play in unison with the voices, or that one part is to be played by a number instruments." ["Chambers's' Encyclopaedia," 1868]
You are not the first person puzzled by the expression "A Capella," or, at any rate, unable to understand it should signify the exact reverse of what it literally does signify. The chorales in oratorios were invariably accompanied, either by double-bass or the whole band. Hence they were, with perfect correctness, said to be performed "a capella." But, as other chorales, sung as part of the church service, were written in the same and simple style the expression "a capella" came in time to be applied to them also, despite their being sung without any instrumental accompaniment whatever. [The Music World, Sept. 11, 1875]
Entries linking to a cappella
early 13c., "subordinate place of worship added to or forming part of a large church or cathedral, separately dedicated and devoted to special services," from Old French chapele (12c., Modern French chapelle), from Medieval Latin capella, cappella "chapel, sanctuary for relics," literally "little cape," diminutive of Late Latin cappa "cape"
The modern meaning of a capella is a myth.
A cappella (/ˌɑː kəˈpɛlə/, also UK: /ˌæ -/, Italian: [a kkapˈpɛlla]; Italian for ''in the style of the chapel'') music is a performance by a singer or a singing group without instrumental accompaniment, or a piece intended to be performed in this way. The term a cappella was originally intended to differentiate between Renaissance polyphony and Baroque concertato musical styles. In the 19th century, a renewed interest in Renaissance polyphony, coupled with an ignorance of the fact that vocal parts were often doubled by instrumentalists, led to the term coming to mean unaccompanied vocal music.(Holmes 2007)
I suppose praise singing or religious worship singing involves instruments, but a song of lamentation alone will lack instruments.