You didn't label your inputs, outputs, grounds, etc...
Is this a balanced circuit? i.e. Do you have "pro audio" XLR connectors (or TRS connectors) instead of RCA connectors? If it's regular unbalanced "home audio", you can cut the number of relays & resistor pairs in half.
You've got a bunch of resistors in series (R1, R3, R5, etc.). That means your audio signal is always going through a bunch of resistors and you can't get to zero attenuation. (You can get close to zero attenuation if the sum of the resistors is small compared to the input impedance of whatever is connected.)
If you look at a standard [u]voltage divider[/u], you should be able to use one resistor for Z2, and switch-in different values of Z1, instead of switching pairs of resistors.
What does K17/K18 do?
Make sure that one relay closes before another opens. Otherwise, you may end-up with a few-millisecond full-volume "glitch" in-between volume-changes.
With any totally passive design, there will be interaction between the voltage divider resistance and the input-impedance of whatever is connected. If the input-impedance is (relatively) high, everything will be OK. But if it's not, you can run-into a situation where you don't get the expected attenuation. i.e. -6dB might end-up being more than -6dB. (At zero attenuation, there should be no problem as long as the series resistance is zero.) That's perfectly OK if you don't need precision.
So.... I'd "feel better" with an op-amp buffer stage at the output, and possibly another buffer at the input. I can understand your desire to keep it "pure" and passive, but personally I'd buffer....
You might consider analog switches as an alternative to relays. You can get an IC with several analog switches in one package... It's a little more "high tech" and less "clunky" than relays.
Or, you might consider a digital pot.