It turns out the files are stores as .EXE's, the likes of which aren't acsessible on my computer, without a program. Any suggestions?
Most Windows applications are .exe files. Are you not running Windows? In that case, why don't you tell us what OS you are using instead of leaving us to guess?
It is probably possible to compile jpsxdec for whatever OS you are using, but most hacking utilities are Windows-only, and if you read a little more about jpsxdec I think you will find that it probably won't help you much with this translation.