System 7.5 does not have a built-in decoding application for BinHex (.hqx). StuffIt Expander is normally used. However, as you already know, downloadable versions of StuffIt Expander are also encoded (.hqx or .bin) or compressed (.sit) for protection, and you need StuffIt Expander for the decoding/decompression....
So, you would have to look for an already decoded/decompressed (ready-to-use) copy of an appropriate StuffIt Expander version (such as 4.0.1 or 5.5). If not available on one of your other computers, such an installer can sometimes be found on early dial-up Internet software CDs or on discs that came with old Mac magazines.
Earlier, with access to a Windows PC (capable of running a DOS program) with a floppy drive, the following was an option:
Prepare an empty PC-formatted 1.44 MB diskette via FORMAT A: in DOS or the "full" formatting option under Windows. Download the MACDISK.EXE file from http://rrzs42.uni-regensburg.de/macintosh/files/macftp.html . Run the MACDISK.EXE (DOS) program on the Windows PC. Follow the instructions on screen. The result will be a Mac-formatted (sic!) floppy that can be used in a Macintosh computer. This floppy contains a Stuffit Expander installer.
Unfortunately, the web address does not appear to be active any more, so unless the page can be found via something like archive.org, this is not going to help.
Otherwise, you may want to try an Apple user group in your area for help.
User Groups - Apple