It is true, the Lord takes no pleasure in the death of the wicked. Therefore, if we are his children, neither should we. Any soul that dies without salvation is a soul created by God but lost to Him forever. Surely that is a cosmic tragedy.
But the passage you refer to in Proverbs is speaking of an individual, personal enemy, not a national enemy. The wording is all in the singular; in other words it is speaking to an individual and of an individual, not to (or of) a group. Thus it is speaking of a specific someone with whom you are at odds. When the person you don't like or who has caused you pain stumbles or falls, you are not to rejoice or gloat. As Jesus said, we should pray for our enemies and those who despitefully use us. But a nation out to destroy your nation is a different matter.
If it were wrong for Israel to have rejoiced when they inflicted defeat on an enemy, the Bible surely would not have recorded such rejoicing in favorable terms. 2 Chronicles 20:27 says: "Then they returned, every man of Judah and Jerusalem, with Jehoshaphat in front of them, to go back to Jerusalem with joy, for the LORD had made them rejoice over their enemies." Enemies refers to those who were out to destroy the main of Israel.
That said, I believe that the teaching of the Bible is that our rejoicing should not be over the death of our enemies but rather our rejoicing should be in the fact that God has delivered us. We should rejoice that it is God's hand that has brought success in our battles, rather than rejoice in the destruction of our enemy. I believe that when our enemies are destroyed, it should cause us to have a holy fear of the power of God Almighty, who can overthrow any enemy, any nation, any power in the universe. Yes, we should rejoice at deliverance from the one who threatens us; but I believe that the Bible demonstrates that our rejoicing should be focused on God, not simply on our own good.
Anyway, just a couple of thoughts off the top of my head.