So to best explain the factory Contour wiring let's start with a pic...
So first off, this pic is upside down. The plug shown at the lower left is found at the top of the rad on the factory set up. There are 2 wires (4 gauge each I believe) coming to this plug. The plug connects via a loomed pair of wires directly to the 12V outputs of the high and low speed relays.
The relays share power from a single 60A fuse that gets its power directly from the + terminal on the battery.
Middle fuse of the 3 in the top left of fuse box image shown (the 3 fuses are 80A, 60A, 60A). The 2 dark relays in the bottom left of image are the 70A relays, yellow one is part of the Contour A/C system. I actually removed the left half of the fuse box and installed in my Mustang.
So, how does low speed work. 12V power from low speed relay goes through plug mentioned above and runs directly to the thermo resistor shown in upper right of first pic (it is actually located driver side bottom corner in the car). The output of the thermo resistor goes to a splice/junction of the high speed power feed and the positives from the 2 motors. If memory serves it is located on the right side of the pic about 8" up from the thermo resistor (the shiny taped section).
The motor grounds are wired to another splice/junction, this time on the left side of the pic, again about the middle and again the shiny taped section. The single black wire exiting the pic near the top left is the ground to chassis for the motors.
With this simple wiring all that is needed is a high and low speed trigger. This can be done with one of many OEM fan switches(various manufacturers - I used VW/Audi unit), with aftermarket controllers or simple toggle switches.
What I suggested above was if you picked up the Hayden unit you listed, that it control the low speed fans (it shows a turn on temp of 185* which should work nicely). As a back up, I would wire the high speed relay to a toggle, just in case. I suspect you may never need it, but its good insurance.