Wiring a Case Fan

What i want to do is take a case fan and mount it into my desk below my laptop (generally due to issues with keeping my laptop cool while running high end games). The case fan in question is the . What i was wonder is providing i took an ac to dc power adapter with the proper voltage/amps would i be able to wire this adapter into the molex connector of the fan (splice the wires) and the fan still preform properly. Would doing this limit the fan to one speed (the one provided by the adapters power) or would the included fan speed controller allow me to still adjust the speed up to the maximum provided by the adapter. This is more of a fall back due to most of the laptop coolers out there being rather a large waste of money and not preforming well, and a case fan would generate much more air flow (in the case of this fan roughly 115cfm).