That's not dissimilar to how I did it, except that I went like:

passive intake -> cabinet -> cooltube -> fan -> carbon filter

So the fan sucks air thru the darkroom louvres, bringing fresh cool air into the cabinet. Inside the cabinet are a couple of 6" circular fans to blow that air around. From there the air gets sucked into the cooltube, through the fan, then is pushed through the carbon filter (which is not visible from the picture). The carbon filter is laying on top of the cabinet, with a pile of books and a small fire extinguisher in front of it, to semi-hide it from view.

The way you posted would probably work though. So you have some choices; there's no 'one right way'.

As for your equipment, sounds good, except I'd probably get a 6" 440-ish CFM fan than the 4" one. Why? Because if you need more fan power, you'll have it. And if you don't need all that power, then you can dial down your fan speed and make it quieter. (A 6" fan spinning slowly can move as much air as a 4" fan spinning at full speed, but does so with less noise.)

Oh yeah, if you're wondering what happened to the ScroG in the picture, well, had to postpone flowering for about six weeks, and the plants got HUGE, blew right past the screen, no way all that vegetation would fit beneath the screen this time.