There is no such thing as a Time picker. You could perhaps use the CC OnExit event as follows:
Code:
Private Sub Document_ContentControlOnExit(ByVal CC As ContentControl, Cancel As Boolean)
If CC.Type = wdContentControlDate Then
If IsDate(CC.Range.Text) Then
If CC.DateDisplayFormat = "M/d/yyyy h:mm:ss am/pm" Then
CC.Range.Text = Format(Now, "M/d/yyyy h:mm:ss am/pm")
End If
End If
End If
End Sub