factors such as: how long the watercolor appears in the film (the less time, the better your outcome), the size within the frame, (smaller is better for fair use purposes) and whether the artist's modifications result in a change in perspective -- that is, a person viewing the watercolor gets a different impression of the subject than they might from seeing the original photograph. There are various cases in which artwork is modified (and a derivative is created) and the results are not considered fair use. (You can read about similar cases here).
What really matters ... It doesn't matter that the photographs are widely available on the Internet or that you are offering your documentary for free. The copyright owner (either the photographer, or the party who commissioned the picture) can still pursue you for infringement. We're not so sure that will happen as the owner may never see your work (and may not care, either). But defending fair use is not something you'll want to do. If you don't want to ask for permission, you should limit the use of the imagery to the shortest screen time possible and (if possible) limit the size so that the image fills only a portion of the screen. That may strengthen your position ... should you need to defend it.