For the most part I think you will be the only one who has this problem. Very few people need to publish Flash projector files for Mac — at least of people who don't have a Mac. And even fewer of those will have 7 year old versions of Flash.
kglad is correct that .hqx is a compressed file. It should be expanded once and the resulting app distributed. You shouldn't be distributing the hqx — to any version of Mac. If the projector was created directly on a Mac, it would just be an app. The hqx format is to get all the bits (that would appear on a PC) across to the Mac where they will show as one app bundle.
Lion dropped support for Power PC applications. So there are probably two places where you are having problems.
Do you get the error when trying to upack the file or when you try and run the app? There is probably some update to stuffit expander or some other unpacking software that will work under lion. Or it is possible that you could upack the hqx on a mac running an earlier OS. The other problem will be once the file is upacked.
Since you have such an old version of Flash it is most likely bundling in an old version of the Flash Player (that is how the projectors work). The old Flash Player has a Power PC codebase.
There may be some way to trick Flash 8 into installing a newer plugin, but I doubt it.
You probably need to update to a newer version of Flash.
