Greetings gentlemen. I happened to stumble upon your forum while looking for other stuff and noticed this thread. I don't know much about ducks, but I am a sailmaker and about a year ago I built a sail for Jim Marsh in Michigan to fit a duckboat that he was restoring. We did a fairly extensive search to see what was historically accurate and didn't find much, but did at least find some old photos of duckboats equipped with spritsails, a few gaff sails and a few lugsails. Nearly all of them had a low profile and a rather drawn-out aft corner, something not found on other types of traditional small boat sails. We weren't sure of the reason for this, but it was distinctive enough that we decided to build one based on that style and cut like a traditional old cotton sail would have been. The fabric is a modern Dacron sailcloth, but it's made in a cream color for use on antique boats where a traditional Egyptian cotton look is desired. My gut feeling is that the long corner may have been a means of getting as much sail area as possible with fairly short, stowable spars while also keeping the sail area low for stability. The rigs that we found were all very simple and anybody who can build or restore a boat should have no trouble building one. Aside from the differences in some of the sail profiles, the rest of these rigs (both the parts themselves and their assembly) are very similar to what you would build when converting a canoe for sailing.
The typical profiles usually looked similar to the sail shown in this old photo. This one is a lugsail, but you can see the long aft (clew) corner that was common to most of the lugs, sprits and gaff sails we found.
http://webpages.charter.net/tbradshaw/Sail%20photos/old%20duckboat.JPG
Even though we weren't completely sure why it was shaped this way, we decided it was too cool looking to miss the opportunity to make one. We went with a spritsail configuration because it's easy to rig and use and Jim had never sailed a boat before. We also kept it's size fairly conservative for the same reason. Here is the finished sail, ready to be shipped out.
http://webpages.charter.net/tbradshaw/Sail%20photos/duckboat%20spritsail.jpg
http://webpages.charter.net/tbradshaw/Sail%20photos/duckboat%20sail%20008%20copy.jpg
...and if it will help anybody, this is the building plan for the sail and it's spars in PDF form, along with the notes I sent to Jim when I shipped the sail. The other parts of the sailing rig which Jim built (leeboards, rudder, mast step, etc.) were basically the same as sailing canoe equipment, adapted as needed for the duckboat. I don't know what percentage of sailing duckboats had sails with this type of profile and I suspect that the intent was more simple propulsion than performance sailing, but it was fun to build something out of the ordinary. Hope this helps.
Todd Bradshaw
Madison, Wisconsin
http://webpages.charter.net/tbradshaw/Sail%20photos/!DUCK.PDF