Reddit mentions of SMAKN SRD-12VDC-SL-C 1 Channel DC 12V High/Low Level Power Relay Module Board

Do you have a cable box or any other device that makes heat 24/7? If so, you might consider wiring up the fans to run 24/7. That's also the simplest way to wire them. Lower temperatures are good for electronic longevity. Fans wear out in a few years, but are cheap to replace compared to a PS4 or receiver.

If you want to trigger them off your receiver, that's pretty easy to do. Most likely your receiver can't power the fans directly (most 12V trigger outputs are 200-500mA output). Some receivers have a switched 120V outlet on the back, which makes this really easy, you just plug the fans in.

Fans can draw anywhere from 160mA (0.16A) to 600mA+ (0.6A)
The Antec fan you linked doesn't have a spec listed for power draw, but typically very quiet fans are below 300 mA.

If your total fan power draw (add together all fans) is less than 90% of the power your receiver can output, you can hook the fans up directly.

If your total power draw exceeds 90% of the rated output of your receiver, you need to use a relay to power the fans.

Here is a relay board that will work.

Here is the same thing but shipped free (probably from China, may be slow)

You'd also need a 12V power supply that provides enough current to run all your fans together.

Here are USB Fans - plug straight into PS4 or TV, and they turn on when the device powers up.

You could also use a 5V relay to control 12V fans from the PS4 usb if you wanted. Or use the TV's USB to trigger the fans whenever the TV is on.

Here is a plug and play thermally controlled fan setup

I'd plan on using both fans as exhaust on the top shelf. Just make air inlet holes in the bottom. Typically you want 30%-50% more inlet volume than outlet volume if you can get it. Remember all the cracks along the doors and edges will let air in as well. Making an air path across the front of the shelf by trimming is a fine idea.

So, step 1, decide when you need the cooling system to turn on - PS4, receiver, tv, 24/7, or other (such as temperature).
Then I can tell you how to use that device to turn it on.

Thanks! I'm in Los Angeles, only electronic components place I can think of is Fry's Electronics: www.frys.com

Would something like this work? https://www.amazon.com/SMAKN%C2%AE-SRD-12VDC-SL-C-Channel-Level-Module/dp/B00MMW0XWY/ref=pd_sim_60_3?ie=UTF8&psc=1&refRID=VZ0TCJ9326VS28VJSDEJ

Thanks again for your help.