Good news, tents are pretty easy to ventilate. Bad news, if you are using a carbon filter then duct boosters won't be sufficient. I was able to use two duct boosters blowing in each side of the bottom to cool a 2x2 8 tube t5 in a 2x2x5 tent, but even that was stretching it once I had ladies in there. I ended up using a 160 cfm 4in "radon mitigation fan" from Menards ($130) and a Y to blow in the bottom of two tents. The cool air coming in the bottom forced all of the heat out of the top. I had my girls elevated on a grate just higher than the air input. This worked for the t5 veg tent and also a 150w I was running in the other veg tent.
With the carbon filter I'd imagine you'll be mounting it wherever it fits! If you had to get clever for space restrictions then you could build an external filter chamber that houses your fan/filter and draws air out of the tent, filters it, and then expels it to wherever you're venting. Take my advice and don't short yourself on your fan for short term savings. Look for something with a good warranty (all of a sudden I've had my 6" for 5 years and I'm still using it; I'm glad I went with the 10 year warranty. Also, the last thing you'd want after you find out how much you love doing this is to have to purchase another fan when you upgrade to some ventilated hoods and a bigger area,. If you'll be moving to vented hoods then I'd go with a 6", my 6" cools two 600w XXXL just fine, my girls can touch glass if they ever needed to...the 4" is not used any more.
Hang your fan with strong bungee cords and eliminate vibration noises
If you always need the air filtered, then run your fan constantly. If you only need to cool/filter when your lights are on, then run a small oscillating fan (probably clip on with your size restrictions....maybe two or three small ones) and not your big fan to save power during your dark cycle. When temps aren't an issue I've heard of people cycling their fans on 30 off 30 to save power, but I like my lights as cool as possible when they are on. Good luck man!