The most sure-fire way is to take an old Dreamcast pad, crack it open, and solder wires to specific points on the PCB. Then connect those wires to your controller of choice. Nothing like homebrew for the customized experience you crave. Unfortunately, getting the analog stick to work properly with this approach is very, very difficult. So if you want to go this route, you pretty much have to settle for digital controls. (as in, on/off only)
Fortunately, the Dreamcast actually lends itself pretty well to digital controls. This is because so many games for it took their roots from arcade cabinets, where digital controls were industry standard for so many years. The best application for this approach is to assemble your own arcade stick. A custom arcade stick is a great thing to have for the Dreamcast.