(I have not yet seen this method documented anywhere, if it's old news then I apologize.)
I accidentally threw away my PS1 GameShark disc last month and set out to find another way to boot backups. Around this time I discovered Free McBoot and read about the PSXLauncher.elf that unfortunately only works on V9+ consoles. After some fooling around I was surprised to find that the ORIGINAL swap trick for the first Playstation still works, but it's much easier to do on the PS2.
What you'll need:
-Any original PS1 game
-Your backup game
-PS1 ImportPlayer Light v2.1 (optional, but will make it easier. It's legal and you can download it here: http://www.megagames.com/psx/psx_utils_bootcd.shtml)
What to do:
1. First off, you'll need to open your PS2. You won't be able to do the knife trick fast enough to make this work. If you have a fliptop, you may be OK, but you won't be able to see the disc slow down so you'll have to time it. Just open the system up to where you can take the top off as well as the DVD drive cover.
2. With your PS2 opened up, start up your original PS1 game and wait for the old Playstation logo to show up.
3. 3-4 seconds after the logo appears, you will see the disc slow down a bit. As soon as you see this, immediately swap the original for the ImportPlayer disc.
4. 3-4 seconds after you insert the ImportPlayer, you will hear the laser softly click twice in a row. As soon as you hear it, swap for the original again and you will be at the ImportPlayer menu.
5. Now just go to start game, and the disc will stop spinning. Replace it with your backup and hit X. Success (hopefully)!
I've been doing this for a few weeks now and have not had any problems, I just try not to be too rough while swapping.
HOW TO SWAP WITHOUT IMPORTPLAYER DISC:
You can do this trick without the ImportPlayer Light disc, but it requires one extra spinning swap. Follow the directions using your backup game instead of ImportPlayer to swap with. When you get to step 4, however, a black screen will appear instead of the ImportPlayer menu. The very second you see the black screen, swap your backup disc back in again. It should load.
Personally, I prefer to use the ImportPlayer disc for two reasons. It will avoid possible TOC issues and also I like how it saves me a third spinning swap.
Here's a YouTube video: [ame="http://www.youtube.com/watch?v=_S6dH_VVjvs"]YouTube - PS1 backups on PS2 WITHOUT PSXLauncher, GameShark or Breaker[/ame]
EDIT: I realize this method is a bit unorthodox, so I figured I'd just let you know that GameShark Lite discs are currently on eBay for $10 shipped. I'm considering getting one but am seriously broke ATM