Feature already exists. Since Word is a Word processor and Outlook is not,
this feature exists in Word, not Outlook. Use the Envelope and Label Wizard
in Word, select your Contact from Outlook. No cutting and pasting is ever
needed.

I have shared your frustration, so I created a vb script (about 50 lines of
code) that will actually print an envelope when an icon is clicked within a
contact.  Essentially what the script does is to take the address information
for the contact and use it in Word to use the envelope printing tool of Word.
The beauty of it is that all onscreen evidence of Word is suppressed.  All
the user sees is a prompt for whether or not to include the return address, a
dialogue box that displays the address information (with a confirmation to
proceed or cancel) and a pop-up box indicating that the envelope is printed.  
If such would be helpful, I'd be happy to share more with you about it.