If you can vent the filter out of the window, it will create negative pressure in the room, which means air, thus small, will not be able to spread to the rest of your house. This is no different to how negative pressure keeps the smell in the tent when it's sealed.
Adding a muffler will pretty much eliminate the noise of your inline fan, which is a good idea anyway, they can be quite loud.
There are any number of ways to make this exterior venting stealthy, and the best solution will depend on the exterior conditions, but 4" is the standard size for dryer vents, and this video shows a simple custom window box for air exchange: