What is the effect of sea-level changes on the extent of the Earth's atmosphere?
90% of earths atmosphere is from 0-10000m this means an increase of 0,001%.

But this is wrong the melting ice will be replaced by air so there will not be any change in volume.

Ice have a larger volume than water have so the result will be a very slight drop in air volume.

I have not taken hight for air under pressure in the ice here but you get the point,You are only redistributing material on our planet so nothing is added or removed from the system.