When reading the whole passage of Zechariah 10;
vv1-3a - The Lord reminded the remnants the days their ancestors' wrong doings that led to the destruction of Jerusalem.
vv3b - However the Lord still care of His people
vv4 - Implying the coming Messiah
vv5 - 10 - Implying the salvation from the Lord eventually reinstated His people and reunited the Israelites.
vv11 - now then why it mentioned Assyria's pride and Egypt's scepter?
In the prophetic books, it has been frequently seen the prophets warned and condemned the evil deeds of the Israelites followed at the end of the book, a promise of salvation, which give a picture of prosperous and wonderful future of them. Did this promise given unconditional?
The temple worship was the core of the covenant between God and the Israelites. It was a main cause that their ancestors worship idols led to the destruction of Jerusalem and the exile of their ancestors. Now the punishment was over, and God will forget their sin. The descendants of them were brought back to Jerusalem, reinstated their covenant by rebuilding the temple. However, since its foundation was laid at 536BC by Zerubbabel, the work had been abandoned for 16 years. God sent Haggai and Zechariah to encourage the Israelites completed the work. Finally the 2nd temple completed in 516BC, exactly 70 years after the 1st temple destruction.
The punishment to the kingdoms who oppressed the Israelites had been prophesized by the earlier prophets. The remnants should see these words realized, that only their God is real, all idols were deceitful (vv2). They should "Ask the Lord" for well being (vv1) by putting God as their centre of living, rebuild of the temple and resumed their worship of the Lord.
Assyria’s pride will be brought down
and Egypt’s scepter will pass away. (Zechariah 10:11b NIV)
Who brought down Assyria's pride? Who took away Egypt's scepter? The remnants should know only God was their highest, their shield and only protection.