You might just have to cut the end off the power for the fan.
Then cut the molex end off the sata cable you have in the second link.
Test the leads to see which ones give you +12v and splice them directly to the fan leads.
I am not sure the adapter you have on the first link will work. I would just splice given the choice. The three position fan speed switch may not give you that much range. The low setting might be all you can use. It is worth a shot. Other wise you might have to do what coderage said and get another type of speed control. I used a PWM circuit on mine.