Fire-Up comes in a Windows and a Macintosh Flavor. There is no such thing as a single application file that will run on both platforms.
This means that you will have to prepare and distribute the Windows version of Fire-Up with your Windows projector and your Macintosh version of Fire-up with your Macintosh projector.

When you author and burn your cross platform CD-rom on Macintosh, things should go smoothly. When trying to do the same thing on Windows, without any Macintosh knowledge or access to a Macintosh, you may get into trouble.

Macintosh application files (except some OSX bundles) will break when they are copied onto a Windows system. Mac applications files consist of a data fork and a resource fork. This is incompatible with Windows or other non-HFS filesystems, and when copied to a windows system, only the data fork is copied. Mac apps will store essential data into the resource fork however. So the file will break.

Encoding Mac applications into HQX format will solve this problem, because the HQX format encodes the data fork and the resource fork into 1 file. That's why a Flash projector created by the Flash for Windows is HQX encoded. The HQX file you get is not an application, it is a Macintosh projector encoded in HQX format!
Some Windows CD burning programs such as CDEveryWhere or MacImage will decode the HQX files as they are written on the CD-rom.

In order to use Fire-Up, you'll have to rename it to match the files you want it to work on. You'll have to copy and rename the Macintosh version of Fire-Up on a Macintosh system. If you do it on windows, the files will become corrupt. It is no problem to copy and rename the Windows version on Mac.

After you have prepared your Mac versions of Fire-Up, you can HQX them and copy them on a Windows machine again. Be aware that creating a HQX file with stuffit, creates a HXQ'ed SIT file, and not a plain HQX file. There is a freeware application HQXing that will create HQX encoded files. unfortunately only for OS9.

Links:

Tutorial on FlashKit: Burn CDs for both PC and MAC from your Windows PC

Excelent FAQ on Flash Projectors and CD Burning