four fair use factors. In addition, because nonprofits compete for donation dollars, the copyright owners may argue that stepping on their rights deprives them of an important source of revenue (and therefore discourages their investing in such footage in the first place). We're also not sure whether the uses you're envisioning are transformative; they're promoting the same message as originally intended -- to shock the public into preserving wildlife. Therefore, we're not comfortable arguing fair use, regardless of the percentage taken.
Some other concerns. A major factor weighing against your legal position is that you are encouraging others to use this footage without authorization. That could be perceived as risky behavior for two reasons: (1) it exposes third parties to the potential for legal action (and they may seek indemnification from your organization); and (2) it opens up the possibility that third parties, with your permission, may seek to subvert your message encouraged by your offering of unauthorized footage. And, as you recognize, this will also certainly jeopardize any symbiotic relationships you may have built up with the larger charities, particularly if they are forced into a public relations dilemma of having to go after those whom you authorized. Maybe it's best to encourage creative individuals to create their own imagery.