Psalm 5:3 is difficult to translate because the verb עָרַךְ has no direct object. Looking at the entry for עָרַךְ in BDAG, occurrences where the object is omitted are seen under three specific contexts: 1/ arranging a battle [1d], 2/ arranging words [1f], and 3/ setting forth a legal case [1g].
Brown-Driver-Briggs Lexicon (emphasis added)
Strong's
H6186
עָרַךְ verb arrange or set in order
1.
d. arrange a battle, i.e. draw
up in battle order, מִלְחָמָה… object omitted Judges 20:22, 23, +
לִקְרַאת 1 Samuel 4:2; 2 Samuel 10:9, 10 = 1 Chronicles 19:10, 11; 2
Samuel 10:17; + אֶל against Judges 20:30; Jeremiah 50:14; 1 Chronicles
19:17a, לְ against Jeremiah 50:9; — Job 6:4 read יַעַכְרוּנִי Di Bu
Du.
e. arrange weapons of army in order for battle Jeremiah 46:3; 1
Chronicles 12:9 (van d. H. 1 Chronicles 12:8).
f. arrange words (מִלִּין) Job 32:14 (+ אֶל against), so (object
omitted) Job 33:5 (+ לְפָנַי), Job 37:19; Psalm 5:4 (probably; > of
arranging a sacrifice); compare recount things in order, יַעְרְכֶהָ
לִי Isaiah 44:7.
g. state in order, set forth a legal case Job 13:18; Job 23:4, so
probably (object omitted) of God Psalm 50:21 (+ לְעֵינֶיךָ), and
(passive of בְּרִית) 2 Samuel 23:5 (compare Dr).
The OP asks, “So does it make more sense to assume that he is still speaking of his ‘voice’ being what he is אֶֽעֱרָךְ־ or ‘directing’?” According to the above reference, עָרַךְ could be used in reference to the arrangement of words. Gesenius' Lexicon, noting the ellipsis, also has עָרַךְ in Ps 5:3 as meaning to direct words towards someone (Gesenius). So yes, Ps 5:3 could mean the directing of the voice or the arranging of words toward God in worship/prayer.
Psalm 5:3 NKJV
My voice You shall hear in the morning, O Lord; In the morning I will
direct it to You, And I will look up.
If we look at the rest of psalm 5, however, there is a narrative shift at v4, with the remainder of the psalm reading like an indictment against the evil utterances of men (vv. 5-6 and 9).
Psalm 5:9 NKJV
For there is no faithfulness in their mouth; Their inward part is
destruction; Their throat is an open tomb; They flatter with their
tongue.
Reflecting on the contrast/conflict between the voice raised in prayer and the mouths that speak iniquity, I suspect that Ps 5:3 may hold another meaning, one that has to do with the context of battle. In other words, he whose voice is raised to God in the morning is as one who is arrayed for battle, with God as his defender and shield (vv. 11-12). Only here, the opponent is the evil that comes from the mouths of men.
Psalm 5:3 YLT
Jehovah, at morning Thou hearest my voice, At morning I set in array
for Thee, And I look out.