Apple used to sell (or recommend, I forget) a half-height rack for academic use of XServes. I know one faculty who got one and didn't realize it would turn his office into a noisy datacentre. He had it moved to a spare office.
Anyway rack-mount equipment is so loud because it all uses tiny fans that are driven at very high RPMs. Using fewer larger fans that spun slower would be much quieter. I would guess that using water cooling might be still quieter but I suspect that would be a lot of effort. Having a single very large fan at the top of the rack, that ran on mains AC, might work fine, assuming the right heat sinks and ducting.
But what I’ve heard about blades is they’re too dense for multi story building datacenters and that sharing blade chassis creates SPoF, and those points aren’t ideal.
https://en.wikipedia.org/wiki/Eurorack
(Unless you just meant a less-than-42U 19" rack, which is easily available. You can buy 19" racks as small as 6U.)