Beautiful!
K&N air filter material (i used them in my first gen crx si) will *NOT* flow nearly enough air with PC fans. PC fans do not create enough pressure unlike auto intake manifold pressure. Look into a simple screen cloth like is on case filters, or use a cut down cheap fiberglass (not HEPA) furnace filter. You are looking for max flow with very low pressure.
The build looks at high risk for a loop of "hot air leaves on the right side and is pulled back in from the fans on the left side since both flows meet at the back of the desk (?? guessing from picture, look like they exit 10 inches from each other then hit a wall that is behind desk.). Is there a way to duct the cold air / hot air away from each other, or will both exit and entry be at the back of the drawer area ? (if you are thinking of a low power build this is much less of a problem). Could the left side fans exit left ? If the right side exhaust fans exit right side your legs will get too warm.
What components are you planning? A simple web surfing computer (low power laptop class) is going to be fine. A 300W typical power gaming system is another problem (gaming in a woodshop is usually 68-85 degrees depending seems interesting. Looking at part schema, etc. on a PC while in a workshop makes sense but dual monitor for that seemed extreme)...
For a simple web surf system consider a laptop. It's already optimized for low power and the brick could be outside the drawer saving 20% of the heat. Customer ducting for input and output air to the laptop exhausts could save you a lot of fans, or the enclosure you have should work fine. (many laptops reverse airflow to their fans to remove dust buildup, so be sure you know which way the air flows if you fan feed the ducts). But a laptop doesn't look good in your window. A power MB + CPU (such as is used in All-in-one builds that don't dump heat well with integrated, not gaming video would drop into that drawer with no effort. Some have external power bricks rather than PSU with fans, that would help also.
Are you using a computer case in the build? If so good - cases are designed to put air flow where it's needed and not have dead air spots. You'd just need to make sure that the case gets cold air into all the input areas, and the output heat is ducted to your exhaust fans. I'm guessing you are not from the neat glass window.
If not using a case for a gaming rig (also good) consider where the PSU output air is going. A duct to your exhaust fan could work wonders. So could mounting the PSU where it's exhaust fan replaces one of your exhaust fans. Look at where the PSU draws cold air and give it a good supply. PSU will dump 50W+ of heat while gaming.
Consider a closed shell video card that exhausts air out the back of case rather than into the case. That could really help if you can line it up with one of your exhaust fans. Nvidia makes some nice ones, and is also the maker of the best video performance per watt video cards. Suggest you use an nvidia Maxwell based graphics card for gaming. They come at a number of price/performance points.
Consider a spot fan for MB voltage regulator (the MB will have a heat-sink on it, you just point a spot fan at the heat-sink. Fear is dead spots on MB components that normally get airflow in a case. Likewise use the intel downdraft CPU cooler not a (better) flow thru cooler (hyper 212) so that it fits in your drawer and so that it blows air down across the memory and MB components. MBs are designed to make this work.
POST PHOTOS when done. Really nice design. If you can say use of the PC people will have fun suggesting low power, heat tolerant components. Fro example, SSDs hate heat (the failure rate goes up with temps), so mounting disk in put airflow would be good. Spinning disk also don't like heat but they are much less sensitive. (I work with enterprise class ssd fail data so this is truth). ;-)