Sadly, just about every "water cooled" computer requires both. Water cooling is rarely anything more than a way to put your air cooling in a more convenient location.
True, but when you can actually have the air cooling with much larger surface area in a convenient location, you can do much better than to just stick a radiator and fans inside or on the side of the case.
I use water cooling to almost silence my gaming "rig". I built a chimney of sorts behind my bookshelf, and have an array of passive radiators hidden there. Also the pump is at the bottom of the chimney, in foam padding. I have a fan at the bottom, and it is being controlled by the water temperature, but the ~250W (guesstimate) that my GPU and CPU dump into the water while gaming can be cooled fairly well with just the chimney effect. It's fairly inconspicuous too, since on the side of the bookshelf the visible bits are the reservoir at the top, the air intake with fan and two tubes coming out of holes at the bottom.
The PSU, chipset, SSD and HDDs need to be cooled by air in the case, so I need fans, but they can turn at a fairly quiet 600 - 800 rpm. In addition to the PSU fan, I use three fans to have slightly positive pressure inside the case, but I could probably do with just a single one if I took the effort to modify the case and make most of the case airtight so I could control the airflow better. The HDDs are suspended and sandwiched, but I think they wouldn't be too noticeable even without the extra soundproofing.
I sunk a fair amount of time and money into this (one needs quality components), but the silence is golden. Maintenance, however, can be a bit tedious because of the amount of coolant that needs to be bled and replaced. Also cleaning all tubing and connections is a chore. With the coolant split into 6 parallel flows for the radiators, filters, monitoring sensors and ports to help bleeding add up to quite a few fittings.
The setup would, of course, be pure overkill if the whole system wasn't in a silent space, but my "office" is an old studio with good soundproofing, so there isn't too much ambient noise. Computer fans do not bother me in more noisy environments, but they really started to bug me in that space. Now if I could just do something to the electrical noises my the components and display make...