Date of composition
Well the first thing I noticed is that your question is based on the assumption that this Psalm was written after Ezekiel's prophecy, but this is most probably not the case. A quick scan of K&D Commentary reveals that most scholars believe Psalm 68 was written during the kingdom Of Israel and Judah, and some even believe it was written during the period of the Judges, yet only Reuss believes that it was written during the Maccabean period, but K&D rejects his scholarship calling it a "violence done to the exegesis".
Hitzig believes it was written during the kingdom of Joram and Jehoshaphat in their campaign against Moab. While Buttcher asserts it is a festal hymn of triumph belonging to the time of Hezekiah, sung during Passover after the king of Assyria left Israel and returned home. Thenius on the other hand is convinced that it was composed to inspire the army of Josiah in his compaign against Pharaoh Necho. They all seem to agree that it is a battle hymn in the style of the Moses' song of the sea and Deborah's song of triumph.
This is how K&D summarize their study regarding the authorship and date of composition for Psalm 68,
But is David after all the author of this Psalm? The general character
of the Psalm is more Asaphic than Davidic (vid., Habakkuk, S. 122).
Its references to Zalmon, to Benjamin and the Northern tribes, to the
song of Deborah, and in general to the Book of Judges (although not in
its present form), give it an appearance of being Ephraimitish. Among
the Davidic Psalms it stands entirely alone, so that criticism is
quite unable to justify the לדוד. And if the words in Psalm 68:29 are
addressed to the king, it points to some other poet than David. But is
it to a contemporary poet? The mention of the sanctuary on Zion in
Psalm 68:30, 36, does not exclude such an one. Only the threatening of
the "wild beast of the sedge" (Psalm 68:31) seems to bring us down
beyond the time of David; for the inflammable material of the
hostility of Egypt, which broke out into a flame in the reign of
Rehoboam, was first gathering towards the end of Solomon's reign.
Still Egypt was never entirely lost sight of from the horizon of
Israel; and the circumstance that it is mentioned in the first rank,
where the submission of the kingdoms of this world to the God of
Israel is lyrically set forth in the prophetic prospect of the future,
need not astonish one even in a poet of the time of David. And does
not Psalm 68:28 compel us to keep on this side of the division of the
kingdom? It ought then to refer to the common expedition of Jehoram
and Jehoshaphat against Moab (Hitzig), the indiscriminate celebration
of which, however, was no suitable theme for the psalmist.
I think given the evidence, it is safe to conclude that it was composed before the Babylonian exile.
Proper interpretation of verse 31
Now we can move on to the exegesis. The original Hebrew is
יֶאֱתָ֣יוּ חַ֭שְׁמַנִּים מִנִּ֣י מִצְרָ֑יִם כּ֥וּשׁ תָּרִ֥יץ יָ֝דָ֗יו
The word חשמנים does not show up anywhere else in the bible (it is most probably a loan word), so its meaning is unclear at best. The KJV chooses to translate,
Princes shall come out of Egypt; Ethiopia shall soon stretch out her
hands to God.
The NJPS however translates it differently,
Tribute-bearers shall come from Egypt; Cush shall hasten its gifts to
In any case, whether you choose to go with KJV or NJPS or some other translation, the implication are clear. Cush and Egypt will pay their taxes and gifts to Israel and they will be Israel's vassal kingdom. So even if this Psalm is describing some Messianic future, Egypt's kingdom will not be independent but part of Israel's great empire. I do not think that Ezekiel's prophecy precludes any such future for Egypt in which the kingdom will have no more independence or autonomy.
Hope this is of any help to you. Just keep in mind Hitzig's words, regarding this Psalm, in the future when you continue studying this complex Psalm, "It is in reality no easy task to become master of this Titan." This succinct remark summarizes well the hardships of truly mastering the archaic language and meaning behind this ancient masterpiece.