You might consider SnagIt to capture the image, or portion of it, from Tableau. SnagIt! Editor will allow you to re-size, crop, and even annotate before copy / paste into your document. I believe that dragging corners maintains the aspect ratio as you describe. SnagIt! might help with other aspects of your document creation.
I currently put my chart(s) into a dashboard viewed on a hi res monitor - and 'display' set to automatic to take advantage of the hi res. Then from the dashboard menu I then export image to png format (which seems to lock everything in hi res) or emf if it might need to be edited in photoshop or other program .
What is a problem for me is if I am working on the road my ordinary res laptop means my exported visuals are ordinary res and I'm working to figure out the optimal protocol to overcome this. I just upgraded to Tableau 8 and I don't know if some of the new features would help on this.
I'm only a novice here to there are likely better more slick solutions!