I'm not sure if FastFind is on the Mac, but when you say "put the FileSaver program in the Trash but don't empty" and "then use FastFind to look for FileSaver, get rid of everything you found", do I drag these into the Trash and not empty it also?.
Putting FileSaver in the trash should prevent it from working, even if the FileSaver extension, which might kick in automatically on shut down, tells it to, as long as the app isn't running when you trash it. But the trash is kind of dangerous as a filing cabinet, for obvious reasons.
Whether FastFind is on the Mac or not isn't really that important. The normal Find — Command F — should be enough to find all of FileSaver. I just can't recall where all the pieces hide. Maybe it's just the app and the extension/extensions.
By the way, how would I compress a file, do I use stuffit or whatever if it's on this Mac, and does compressing isolate the files/apps and stop them from working?
Stuffit is pre-OS X's de facto standard, so you might have it or DropStuff, which was a Stuffit freebie, and which might still be around on the net for your OS if it's not in the machine.
Compressing an app makes it unrecognizable to the computer. Its code is squashed.
After compressing, you'd have to trash the uncompressed version of the app, if Stuffit's preferences aren't set to delete the original automatically. Mine isn't, because if the system freezes in mid-squash, both versions might be lost (OS 9 is very last century.

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I haven't got Norton Disk Doctor on CD but can track one down if needed.
With only a single drive or single partition, Norton Disk Utilities can't fix anything, because it can't repair or properly defragment the system that's running it. That's why I have two OS 9 partitions (I've lost the Norton CD.) I have to run Norton off one OS 9 partition to fix the main partition, but doing that is at least 10 times faster than running the CD, so I don't really care.
But if you don't have Norton on CD but decide to kill it anyway, you could back up all the Norton stuff and its extension/extensions and still have it if you partition the drive or add another one.
Stuffit Deluxe can compress, then slice up big files, such as apps, into multiple pieces small enough to fit onto floppies. It can then rejoin them when the app is uncompressed. (But don't forget Norton's extensions.) If you do this, copy the pieces onto more than one set of floppies. They are notoriously unreliable.
I wouldn't want to run my main OS 9 partition long-term without Norton. (Or DiskWarrior. Norton has very occasionally failed to repair the disk.)