I have basically the same space and I use muffin fans to vent the space but no filter. One 3" and one 4". About 75-85 cfm together.
You could easily mount a 4" can fan, but on the outside would be better to save space. There are combos, for less than $100 out there with a carbon filter. Good for upgrading into a bigger space later......
Honestly, pc fans aren't terrible for smallish spaces. I use to, duct, an entire 4x 8 cabinet with all pc fans. But most even with good cfm ratings will have terrible back pressure when a filter is placed over them. It just takes some work looking for the right fan and then some of your hard earned loot too...
Honestly, if you can afford to go 4" fan/filter combo do it. I like S+P because some are adjustable speed [which is rare] and good fit for small spaces but the 4" is going to run around $65 just for the fan.