The Arctic is already float ice, which means that its melting will not raise the sea level (caveat later in this post). The ice displaces exactly the volume of the melted water. That's the basic physics of the deal. Only ground based ice can raise the sea level by melting. However, the Arctic Sea, when ice covered, reflects a whole lot of solar energy due to the white ice and snow. When that melts, the albedo (the amount of solar energy reflected back) is much lower. That heats up the Arctic Ocean and, as everybody knows, increases the sea level due to expansion. But the ice melting has no effect other than that.
It's complicated. What we really need to worry about are the Greenland and Antarctic ice fields, both land bound. They are both going through a bit of collapse. It will take many decades, but if it goes the way it seems it will go, people had better think about where they will move when the shorelines are under water.
Just a little correction to your post.
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