Working with the JIRA instructions, I've been able to change the Online Help link to local documentation files with the Backup/Restore function, but Fisheye doesn't seem to have instructions on how to do that. Is there a way to change the Help link to stop trying to look at the Atlassian website and use local documenation too?
Currently this is not really designed to be configurable. It is possible to do this by overriding the classpath used to run FishEye.
FishEye gets its help paths by using a resource file in the fisheye.jar file known as help-paths.properties. This file has the URLs used for documentation and the names of various pages within the Atlassian documentation system. If you were to extract this file and put an updated copy into its own jar you should be able to change the URLs. This jar would need to be added to the startup fisheye classpath before fisheye.jar. This requires a little futzing around since fisheye is launches with a -jar argument.
There is a more information on the FishEye help system here: http://blogs.atlassian.com/2007/12/using_a_wiki_fo/
A note of caution: Such a customisation would be considered unsupported. The underlying mechanism could be changed in upcoming releases. Even if the mechanism is not changed, you'd also need to track updates to the help-paths.properties file as you deploy new versions.