Pure boot disk only works on the original PSX with a product called PSX-exchange... or something like that... PSX-change???
Note, I haven't tested it that way, so I am just assuming it works.
As for PS2, I think there may be a external USB mod with a boot disk... have a look around.
No that I think about it, there is also a product where you replace your PS2 cover with a flip top lid allowing you to swap games without ejecting. But it too uses a boot disc.