The keyboard shortcut for inserting the current date into a Word Document is ALT+SHIFT+D. The problem is that the inserted date is a live filed, so it is being updated every time you open the document.
To insert the current date without it ever being updated (that is, to insert the current date as simple text) – press CTRL+SHIFT+F9 when the cursor is inside the added field.
So, to add the current date as simple text:
press ALT+SHIFT+D > press the left arrow (to stand inside the field) > press CTRL+SHIFT+F9.