To supplement
this post I will add that you need only sever the two wires of the stock fan, then solder in your new 2-wire fan. The old fan did not have speed control, and you really don't need speed control on any new fan if it is as quiet as the 60mm Silenx fan I used.
To make your connections professional and robust, I recommend cutting two 1-inch lengths of heatshrink tubing first. Then cut the stock fan wires, slip a tube on each wire, then trim the insulation off the wires, solder them to your new fan, then slip the heatshrink over your soldered contacts and heat.
This photo shows the very bottom of the stock Elina fan at top. You can also see the red & black wires twisted together, coming from the fan and leading back to the analog board.