I would like to add documentation for bash functions so that users can lookup the functions with man. There should be no visible difference between my functions and actual commands.
I know I can do this by overriding man with a function that checks for my own functions. Is there another way?
Real shell functions are not documented by individual man pages but by the help builtin command. You would have to override that. But even I would not look there for information.
Just generate normal man pages and throw them into /usr/local/man/manX or /usr/local/share/man/manX - whatever your distribution already provides. Check /etc/manpath.config that this directory is already mentioned there. That way no one must fiddle in their startup files with the MANPATH environment variable.
Each manpage should also contain a clearly visible section explaining, that this is a function and not a command and what the difference is.
After that the social part kicks in: Tell everyone at every occasion about that documetation. By every I mean every, not only suitable. :-)