It's not just a matter of knowing the pinout, you also need to know the protocol. Almost all systems that don't use the de facto Commodore/Atari one/two-button stick pinout have a protocol of some kind to reduce the number of wires, so you can't just rewire the pad into a new connector and use it on another system (NES to/from SNES notwithstanding). PSX's protocol is one of the more complex ones, as it's designed to be expandable to future controller types as well as for interfacing with memory cards. That's not to say that it's impossible to adapt it to other systems, just that you probably can't do it with a handful of standard logic chips (well, maybe if it was literally a handful...). There is a page floating around with detailed PSX protocol information, and I think Gamestation X has a local mirror of it, so this isn't totally hopeless by any means. Their Saturn controller page, however, contains no Saturn controller information at all - what's there seems to be an overview of the 3DO protocol. I'll dump what I know about the Saturn protocol here.
The Saturn interface uses 9 pins: 2 power pins, 3 control pins, and 4 data pins. The control pins are used to tell the controller which set of data to present at the data pins - it is a multiplexed parallel interface rather than a serial interface. It's essentially an expanded version of the Genesis/Megadrive controller interface. The data pins are called U, D, L, and R, presumably because they present the directional pad by default. The control pins are called TH, TL, and TR. Only two of these (TH and TL I think, but I'm not sure) are used on a standard Saturn pad, so some pinouts label the other one as a second 5v supply. Anyway, two control pins allows addressing 4 sets of data, or 16 buttons. So, to read the Saturn controller, the system cycles through each combination of the two control lines to read all four sets of data. This part of the interface should not be difficult. However, IIRC there is also an identification phase, which might require a little extra effort. Once my PC is set up again, I'll dig into the SMPC manual and see what I can find...