Thanks a lot Christopher to answer with an AppleScript code of Shane Stanley (perhaps you adapt) 
Even if I am still running OS X 10.10.5 Yosemite, it was hard to resist to give a try 
I was first locked by the statement
AppleScript cannot coerce datePicker's dateValue() to be a date (don't know if it is due to Yosemite).
Nevertheless, some Googling and do-it-yourself leads to a solution with help of Shane Stanley anew
I even manage to test ability to preset initial date to a given one and use a more compact display
Here is the Yosemite working starting point demo to a more sophisticated code needed to be actually usable
date-picker-yosemite-preset.applescript.zip (1.5 KB)
Another good new is this text code with extension ".applescript" can run within KM using simple Execute action
I have two more questions to kind Object C specialists:
- How to display
01/04/2016in place of1/ 4/2016? - How to make ↑ ↓ to increment/decrement within KM... as it works nicely outside?
--Alain