The girls are looking very happy!
I worked in HVAC for about 20 years,and I know that inline fans can be noisy things-
I wish I had some advice as to how to quiet them down,but in my experience with them
it was never needed-Generally,with any fan that moves a lot of air,you're going to have some noise,
and muffling it will restrict airflow to the point of making it almost useless.
You could run a length of ducting from the outlet to under the bed maybe,where the noise would be
somewhat absorbed by the bedding,but that would sort of put a dent in the "stealth" aspect of your cabinet.
Smooth ducting is quieter than flex ducting,but in your application it would be tough to use anything but flex .
Using a speed controller on the fan is another option,but the slower the fan runs,the less air it moves.
Hopefully, someone else will chime in here with more ideas,and more experience with quieting inline fans.