I wanted to use the system date format for consistency, rather than programming it into the shortcut.
It takes about 30 seconds to set up.
In Automator (Applications folder)
New service
Receives no input in any application
Drag Run Applescript from the Utilities section on the left into the right pane
Check Output replaces selected text at the top of the right pane
In the Applescript window replace all the text with
on run {input, parameters}
set _date to short date string of (current date)
tell application "System Events"
keystroke _date
end tell
end run
- Save the service as Short Date workflow

In System Preferences > Keyboard › Shortcuts
Click Services on the left
Short Date will be listed under Text in the right panel
Add a key combination for the new Short Date service

In System Preferences > Lanuage & Region › Advanced
Click on the Dates tab
Modify the Short: format as desired
Click OK

Note: this system depends on the Services menu under the Application menu. When the menu is not accessible, the service isn't either. It does not work, for example, in the open and save dialog.
tell application "System Events" set _Date to (current date) keystroke ¬ (year of _Date as text) & ¬ text -2 thru -1 of ("00" & ((month of _Date) as integer)) & ¬ text -2 thru -1 of ("00" & ((day of _Date) as integer)) & ¬ text -2 thru -1 of ("00" & ((hours of _Date) as integer)) & ¬ text -2 thru -1 of ("00" & ((minutes of _Date) as integer)) & ¬ text -2 thru -1 of ("00" & ((seconds of _Date) as integer)) end tell
– unmultimedio Mar 05 '20 at 20:47