To complicate matters further, Fulton and Livingston made changes to the boat almost immediately after its first voyage. Even Fulton's patent drawing images are not of the first boat-- instead, they reflect the early changes made in the boat.
Our best knowledge of the actual appearance of the North River comes from a variety of sources, taken together: Fulton's drawings and sketches, Fulton and Livingston's letter's, written accounts, etc. All of those sources were used by Randy Decker to create a wonderful model of the North River for the exhibition "Bobs' Folly" in 2007. The model took over 750 hours of labor, and, at the time of its creation, was the most accurate known model of Livingston and Fulton's boat in 1808 (after the first voyage, when it had been enlarged). Here are some images:
View of the bow:

The paddle wheels:

The boiler:

I wish I could achieve that level of detail and accuracy on the cat! Alas, the material I'm using for the cat (and time and skill!) don't allow it. Randy used special scaled lumber, laid board by board, and hand-crafted many of the other elements. For the cat, I am looking for special small nails for the rivets-- any suggestions on where I can find some would be greatly appreciated!
After the exhibition's conclusion in 2007, the model has remained on exhibit in Clermont's visitor's center- go check it out! (Soon, it will also be joined by a working model of the steam engine.)