My build is somewhat different than yours and not really a solution, but thought the info might come in handy since it's first hand experience. I've done a 10 watt chip array build with a heatsink/fan for each LED & rather than wire them separately, I decided to solder the fan leads directly to the LED terminals. Like yourself, I'm attempting to save on extra wiring & hardware as far as this is feasible. The heatsinks come with the fans which run on 12VDC. The reason I went with 10 watt LED arrays is that most of them require in the neighborhood of 9 to 12VDC forward voltage to run at maximum current of 900-1000mA. I have a 250watt 12VDC power supply providing power to the fixture through manual dimmers. As I mentioned, somewhat different than your set up & you'll need a separate power supply to run your fan, since meanwell drivers won't provide the voltage/current to properly drive your fan. DWZM has pretty much spelled out your options in that regard.
I decided to give my scenario a try & so far it's working well. Worst case I can cut the fan leads off the LEDs, rewire them to a dedicated 12VDC supply & run them at full speed. At the moment, since the fans are slaved to the LEDs, they run slower when I dial the voltage down & faster when I bump it up. The drawback is that if I start the LEDs on a very dim setting in the morning, the fans need a kick start to get them turning. Once running they will keep spinning with the voltage all the way down to approx. 3 volts, albeit very slowly. Fortunately at that voltage, the LEDs don't need the fans since the heatsinks handle the minimal heat produced at that setting. Once the voltage is up around 5 to 6 volts, the fans spin at a good speed. As far as noise, I've actually found that the fans are quieter at full speed. Some of them have a mildly irritating whine at low to medium speed which disappears when they're closer to running full bore.
Looks like the fan you're needing to run is somewhat larger, so it will more than likely require a voltage closer to 12 volts (like DWZM says, 9 volts or higher) to get the mass turning, so again, my hookup is not a good comparison, just to give you an idea what happens under somewhat similar circumstances.
Here are some photos. My setup is a parallel hookup with the power supply providing a regulated DC voltage to each individual LED/Heatsink/Fan combo. I find it much simpler than the constant current, series hookups more commonly used to DIY the 3watt LEDs.
