PS1 controllers ARE compatible with the PS2. However, the difference between the Dual Shock 2's and the PS1 controllers is that the Dual Shock 2's have all analog buttons. Every button and both joysticks are analog (except the directional pad...I think...don't quote me on that). On the PS1 controllers, all buttons were digital. So to answer your question, you can still use a PS1 controller on a PS2, but you lose analog use for the games that need it. An example is Metal Gear Solid 2, you can peek around corners using the shoulder buttons. Because the PS2 controllers are analog, the harder you press the shoulder button the farther Solid Snake peaks around the corner. Now with a PS1 controller you can still use the shoulder button to peek around the corner, but there is no analog feel to it. Only digital. Yes. No. On. Off. 1. 0. Nothing inbetween. So you can still play the game, but you lose a little bit of the experience by using the PS1 controller. But the advantage for you is that the PS1 controller would be WAY easier to hack.
Jakobud