PS2 swapping is a bit strange.
It reads the size of the first disk inserted - in this case the game shark. If the disk you swap in has a larger file table than the boot disc, it won't work. (Through the lid)
Best software to use for swapping is breaker pro. It's another cheat system like game shark, but it was designed for swapping, and has a max size file table - so will boot anything.
Although you say you can boot US ps1 games with this method with no problems?
Edit - I'm a dick - is it a ps1 or ps2 game shark? I assume ps1 - then not sure the above actually counts. Breaker pro comes with disks for ps1 and ps2 swapping, so it might still be true.......
If you can download the iso of breaker pro ps1 disc, you could try the double swap. Game shark -> breaker pro -> raiden