Great Question and we do appreciate you asking it here in the forum.
In the past, it was common to hear of gutter downspout pipe being used in a 2x4 wall, to vent the dryer. But now a days we do not hear that much. Also, it was common to find a 3x10 rectangle pipe with the same connection of round to rectangle that you explained. Both of these are very inefficient and usually leave a "pocket" for the lint to fall down into at the bottom.
If one of the reasons for going through a retro install of a dryerbox is to move both appliances back maybe 5 inches, or to make the dryer run more efficiently, or both, then it is worth the effort if some of the conditions are right.
The scenario number 10 of 16 at the bottom of this page: http://www.dryerbox.com/photo_gallery.htm
is of a 2x4 wall that had no vent pipe, but had 4-6 feet of working room height in the attic just above so we were able to first confirm there were no obstructions, then cut the top plate out, and send 5 foot sections of round pipe down the wall. Yes, 4 inch pipe fits and works, it’s just deformed a bit to oval. The person at the bottom reached up through the dryerbox and steered the hard pipe into the dryerbox port. It was amazingly quite easy with two of us and room in the attic. We then installed a DryerJack (roof vent) www.dryerjack.com
and the homeowners were very happy.
Make sure you look at that link above, and any other similar retro installs on that page. I'd also very much like to get your before, during and after pictures of the install if you elect to tackle it. I will be happy to discuss this further on the phone if you have more concerns. Thanks and good luck.