Given an alcohol solution and a mass of ice in whatever shape you like, is shaping it into a sphere the worst possible way to cool your drink without diluting it?
If the ice starts off at a sub-zero temperature, it is able to cool the drink without diluting it by first warming to 0 °C. After the periphery of the ice hits the melting point, it then waters down the drink in order to absorb more heat. However, if the conduction isn't perfect within the ice, melting could occur before the whole ice cube hits 0 °C, which seems sub-optimal.
I don't know if because it's not just water that's being cooled the thermo changes, or if there's some other important effect I'm neglecting