Earlier quoted context omitted.
If your fans are noisy buy better fans. We had some corsair fans that came with the AIO at work, replaced them with noctuas and the computer went from mildly annoying to dead silent. Though with water cooling you might also have a lot of pump noise, especially if the radiator is mounted incorrectly.
If your fans are noisy, buy BIGGER fans. The larger the diameter of a fan, the lower the RPM it can spin at to move the same amount of air (same cooling capacity) as a small fan. Provided you can put the air where it's needed (e.g. a 1 foot fan can't "focus" air onto a 6 inch radiator) a larger fan will just about always be quieter and more efficient. Oh, and having a water cooled PC with the radiator and fan inside…
And historically, bigger case fans have been problematic, those 200mm fans they tried to introduce some years ago. Bad static pressure if I recall correctly?
Also, I wouldn't call having a radiator and fan inside the PC silly. The case eats a lot of the noise already, it's the easy and the common setup, and good AIOs are quiet and cool well. But maybe you just wanted to share a cool big water cooling setup with everything noisy routed into the basement ;)