It would be prudent to monitor the cables as they are released for any mentions of your organization and its activities. While personal names are being redacted, there is no guarantee organizational identities will be removed. The main security concern is depending on the context in which an organization is mentioned, groups may erroneously perceive some type of affiliation with USG, thus increasing risk - ranging from potential negative publicity to targeted attacks on facilities and/or staff. At the present there is a Web site that allows you to perform keyword searches of all publicly released cables. If the site is taken down, it's likely others will take its place and I'll update the link.
One other thing to mention. An encrypted, gigabyte-plus "insurance" file containing the unedited cables and other unreleased material has been available via BitTorrent since October. If anything happens to Julian Assange, supposedly the encryption key will be made public, providing anyone who downloaded the file with the raw information. Whether this is a bluff or not, remains to be seen. If the data is released, it's a forgone conclusion media outlets and both political and armed anti-government groups will be promptly mining it.
PS - USG has warned federal employees that since some cables are still classified, reading them is breaking the law. No word on if or how this stance may apply to organizations being funded by USAID.