First, presuming this cabinet is presently, only passively cooled, a mere one fan at low RPM will do a lot- don't go thinking that you need multiple fans or full speed because odds are good that you don't unless you room temp is quite high and then for the inhabitants, an air-conditioner is a better plan.
The easiest way is to grab some wall-wart, but therein lies the details. Suppose you grab a common 12V, 500mA unregulated wart. You most likely to not need to put 500mA into fans to cool this, so the warts are essentially going to be floating high(er voltage than 12.0V). There are formulas one can use to try and predict the exact resultant voltage once they have the other variables resolved, but some are only resolvable in use, for example the true transformer output as they are not what you'd call "high precision" devices, are subject to a few percent deviation from the labeled rating.
Anyway, the best way to go is use the largest diameter and thickest fan possible and reduce it's RPM as much as possible. Put the fan opposite the exhaust path and control the exhaust such that it passes by all components.
Then the strategy is to control current, not voltage, because a voltage control (and therefore only indirect current control) can cause pulsating as each winding on the fan motor is energized in turn and the sudden current surge causes a sudden torque increase, which is also bad for the bearings over the long-term.
Since we can't yet know just how slow the fan(s) can run and remain sufficient to cool this, I can only give you a ballpark estimate, or an example if you will...
If you had a 12V 500mA DC wall wart, and a 0.12A fan (as labeled, actual amperage used can vary from the label depending on methodology to attain the rating), you might want to put about 68 Ohm 2W (for more heat margin than 1W) power resistor in series with the positive fan lead. An LM317 or similar IC regulator in current-limiting mode would also work, but need a limited output filter cap size and frankly the additional 30 cents cost and even the trivial additional complexity is entirely unnecessary, only makes sense if one had a drawer full of regulators but no power resistors on hand.
You could just try a lower voltge wall wart instead, possibly a 5V wart would be a good match (keeping in mind that it too, if rated at higher current than the fan's rating (give or take) will be at a higher voltage. You could use a regulated switching wart instead, but unless your only goal were to run the fan at as close to 12.0V as reasonably possible, the detractions outweigh the benefits... unless as above, you happened to have them on hand already but nothing else. Then again, a 12V 500mA unregulated wall wart can be had online for about $3.
Keep in mind that the supply should be kept away from the other audio/data cables.