This is all using burned discs, not USB.
You can play PSX backups on older PS2's using a disc based PSX GameShark (or Action Replay, depending on the country) to do a disc swap. Later versions block GameShark, so...
You can play on later PS2's using ulaunchelf and an original PSX disc to do a disc swap. For some reason this doesn't work on older PS2's.
Of course, on pre-slims you need a way to get at the disc to swap it, either a slidetool, a fliptop case mod, or a solder free eject button mod. On slims you need a way to hold the lid sensor down.
The GameShark method, you just wait for the Gameshark to load, then either choose your codes or don't (up to you if you want to use codes), then swap the discs (the disc spins down so this is safe) using whatever method you have to change discs without the system knowing you ejected the disc. Then you just tell the Gameshark to start the game (with or without codes, doesn't matter).
I use the solder free switch mod, but any method should work. I use the Gameshark disc for PSX games that came as a free bonus with the PS2 Gameshark, but I don't see why Gameshark Lite or other disc based Gamesharks wouldn't work. Obviously the hardware based Gamesharks won't work because there's no parallel port on the PS2. It has to be a disc for PSX games, though, that's important, if you use a Gameshark disc for PS2 games it won't work.
The ulaunchelf method, get into ulaunch elf however you want (you can get in there from FreeMCboot or on a 90000 series slim using a FreeMCboot card and a Swap Magic 3 disc -- it won't launch FreeMCboot but will start up ulaunchelf.) Then put in an original PSX game, only make sure you DO trip the sensor so it reads the disc change (if you used Swap Magic) or just that you've put in a disc at all. After it stops spinning, take out the original disc and put in a backup disc, this time you must NOT trip the sensor. Tell ulaunchelf to load the disc.
These are the methods that work for me repectively to play PSX backup discs on my 30000 (v4) PS2 and90000 PS2 slim.
I think you can on a Cfw PS3, but then you need swapmagic, and you need to do it twice and all that crap and it's too much effort for just one go on Crash bandicoot.
On a CFW PS3 you rip them to the hard drive and load the iso in multiman.
The PS1 side of a PS3 is completely emulated, I think
Correct, which is why I prefer to play my PSX backups on my PS2.
you need to repeatedly swap it, more than just the once, so that the PS2 doesn't get wise to it during the loading process
Not with either of the methods I've mentioned, you don't.