Hi Janos, with the foreword that I know very little of technical details, I've read and have been told that for chrono movements it is not the same as for 3-hand ones where you can simply "hide" the date window with a full dial.

In fact the most common chrono movements (V7750 and its family, L5100 and its family) do run a serious risk of getting damaged if one changes the date manually (i.e. not by advancing the hands) in the "wrong" period, usually from 9.00 PM to 3.00 AM of the following day. Most user manuals take great care in recommeding that this be avoided in fact. It is safe to assume that the same would happen to cal. Heuer-03.

Now, with no date window (and no 24 hr indicator on the dial) this may well happen by mistake - and boom, a damage is done that requires disassembling the movement etc.
In fact in those rare cases where they've chosen to omit the date from the dial on a date or day-date chrono movement - e.g. the Sinn EZM1 "Bape" version opposed to the regular one - the watch manufacturer also physically removed the date wheel altogether.
Which means a more invasive approach than simply swapping a dial in the assembly line I am afraid - still feasible of course, but not so simple.
Cheers,
Fabrizio