This replay is also just for the others who may be interested in this (I first tried the public forum before entering a support ticket) :
I don't use databinding but each datapoint value is updated explicitly in code. I simply worked around the zero-label problem as follows :
dataPoint.YValue = newValue;
dataPoint.Label = "";
dataPoint.LabelFormat = (dataPoint.YValue != 0) ? "#Y" : "#LABEL";
This hides all "0" labels from the chart. Should have thought about that from the start...
In attachment a screenshot of the charts before and after codechange.