Some things are more fun than work...
This works in an open message - you need to select the date in the message and run the macro (its not fully automated). 3/10/16 works as does 3/10 or the full short date 3/10/2016. the format can be tweaked as needed. Examples:
objSel = Format(myDate, "dddd, mmmm d, yyyy") returns Monday, April 11, 2016
objSel = Format(myDate, "ddd, mmm-d-yyyy ") returns Mon, Jul-11-2016 and adds a space at the end
It might be easier to use an inputbox - much like the insert date dialog, you'd trigger the macro and enter a date in an dialogbox instead of typing it then selecting it and running the macro.
basics of using a macro are here -
How to use Outlook's VBA Editor I'll write this macro up as an article because it's kind of cool.
Won't be before the weekend though, because I'm supposed ot be doing something else right now.
Code:
Sub CopyPasteDate()
On Error Resume Next
Dim objItem As Object
Dim objInsp As Outlook.Inspector
Dim objWord As Word.Application
Dim objDoc As Word.Document
Dim objSel As Word.Selection
Dim myDate As Date
Dim DataObj As MSForms.DataObject
Set DataObj = New MSForms.DataObject
Set objItem = Application.ActiveInspector.CurrentItem
Set objInsp = objItem.GetInspector
Set objDoc = objInsp.WordEditor
Set objWord = objDoc.Application
Set objSel = objWord.Selection
objSel.Copy
DataObj.GetFromClipboard
myDate = DataObj.GetText(1)
objSel = Format(myDate, "dddd, mmmm d, yyyy")
Set objItem = Nothing
Set objInsp = Nothing
Set objDoc = Nothing
Set objWord = Nothing
Set objSel = Nothing
End Sub