I found a work around.
Since I am really using autohotkey (ahk) to write my "UDTs" and "assign" my own hotkeys, I use ahk to do a "controlclick" on the checkbox of the start-date field in order to disable it, however, since it could be the case that the task's start date is aleady disabled (which would then cause the calendar pop up to come up), I make sure that it is enabled first by setting the task's start date to some value by means of the command line switche "-sd" (I use todays date but ahk could also read out the current date the field is/was set to). Then, since the focus now is on the date field, I set the focus back to the control where focus was to begin with (also using ahk). Sounds a bit messy but actually works quite well and even quickly so far. (The only optical downside is a short flicker of the start date checkbox.)
For sure, this would also work with the due date field.
Regards, S.