On those Hydro huts I thought that they came with a 6" duct for fans? Also, I thought most air cooled 1000w's also cam with 6" flanges. I think that your 4" might work, but I think that it is a big might. Just be ready to have a back up plan.
Maybe try this, use the fan/scrubber on the grow chamber it self, because you need to focus that scrubber on the chamber because of smell and of coarse heat, and then get a $75 Squirrel cage fan for the hood of your light.
The bucket idea is pretty good. Just remember the bigger those plants get, the harder it will be to swich them out to a new res.
Good luck
Adieu