I would like to modify the style of Print in a Mathematica notebook. Locally, I can do so by toggling on Show Cell Expression of some output of Print (i.e. in some cell generated by the command), adding ShowCellLabel->True and modifying CellLabel->"mylabel".
This works for a single cell and I would like to make this change for all cells of the notebook. Hence I edit the Stylesheet and paste the section Local definition for Style "Print" from Default.nb -> Core.nb to the private style definition of the notebook.
If I now modify this particular style (editing the cell expression in the style definitions), I can e.g. successfully change the margins of all Print cells in the notebook. I can also toggle on the labels using ShowCellLabel->True, but I can NOT modify these labels. Any command CellLabel->"mylabel" is simply ignored in the notebook. Instead, the label During evaluation of In[.]:= remains.
How can I change the cell label using the stylesheet s.t. it applies to all Print cells?