You can cut (with a hack saw for tin) flush against the wall (exiting out of the basement).
Then with rigid metal ducting (with an end that is slightly tapered) extend from the newly cut flush with the wall out straight past where the new drywall will be.
Attach a 90 degree angle in the downward position and connect the flexible metal duct to the 90 degree angle.

I hope that makes sense.

If you have a 6" inside-dimension clearance between the exterior wall and your sheetrock, you have more options than most:

1. Use 4" round rigid-steel ducting.
2. Use flat rigid-steel ducting (more difficult to find).
3. Use flat rigid-steel "periscope" ducting.
4. Use a dryer duct exit panel.

Whichever you choose, don't bury flexible ducting in the wall--you need to use rigid-steel ducting for in-wall installations.

Here's links to all except the flat rigid-steel ducting:

Standard 4" round rigid ducting:
http://www.homedepot.com/p/Speedi-Products-4-in-x-60-in-Aluminum-Rigid-Pipe-26-Gauge-EX-26AP-460/202907098#.Ubp0aee1FQg

"Periscope" ducting:
http://www.homedepot.com/p/Whirlpool-29-77-in-In-the-Wall-Dryer-Vent-Periscope-4392892/202647858#.Ubp0F-e1FQg

"DryerBox" exit panel:
http://www.dryerbox.com/index-confirmed.htm

Thanks very, very much for the suggestions!