Hi Yves,
The only way I can think of, to do what you're trying to do, is first to make the label visible on front panel. Then you do the regular control copying. The new controls will have their labels visible in both front panel and the block diagram. When you're done, open a reference to the VI, get the reference to all controls, then use a property node to set the visibility to false for all controls (or if you only want to change the property for certain controls, check the control label name and if the label is "numeric *", then change the visibility to false.)
There're ways to modify front panel objects, but I do not know of any method to modify the block diagram objects programmably.
Hope this helps,
Dan