You can build any of the boats in the Designs Menu link below using wood as a
framing material. It doesn't matter that they are shown as aluminum frame
folding kayaks. Check out the "Gallery" in the Wood Frame Manual to see these
same boats built from wood with sewn or PVC skins.

http://yostwerks.com/DesignsMenu.html

You can skin the boats any way you want...including sewn nylon and the
coatings of your choice. The Sea Rider, Sea Ranger, Sea Raider, Sea Cruiser,
Sea Tour 17, and others have dimensions close to your requirements. Above all,
read the "Wood Frame" construction manual before starting. Finishing by
Wednesday may be unrealistic , so take your time and enjoy the process.

The attached pic shows a wood frame Sea Ranger with sewn nylon / urethane
skin built by Matthew Keller. The boat is 17.5' X 19.5" X 28 lbs.

Tom