Interesting, I haven even thought about looking if alsamixer is available in Chome OS, udev tools are also available. You should try to create a udev rule to ignore this device as described in Tell PulseAudio to ignore a USB device using udev by Jamie Nguyen (or blacklist the kernel module, suggested further below):
Create a udev rule
Your system should have udev rules already defined in the /lib/udev/rules.d directory, such as 90-pulseaudio.rules. There should also be a /etc/udev/rules.d directory where you can define your own rules.
The rules are parsed in lexical order. Create a file called /etc/udev/rules.d/89-pulseaudio-usb.rules, so that it’s parsed just before 90-pulseaudio.rules (though you may have to experiment with the numbering if things don’t work as expected).
Open the file in your favourite editor and create a rule. Use the idVendor and idProduct numbers from earlier to uniquely match your USB device, and then set an environment variable that tells PulseAudio to ignore the device:
ATTRS{idVendor}=="1852", ATTRS{idProduct}=="5110", ENV{PULSE_IGNORE}="1"
[…]
Reboot your system and PulseAudio will no longer acknowledge that your USB device exists.
… or How to reload udev rules without reboot?
The problem of course is that you are not asking about a USB device, it's likely to be HDMI. The following rule might work but I have not HDMI audio capable device to test:
SUBSYSTEM=="drm", ACTION=="change", ENV{PULSE_IGNORE}="1"
You can also try to blacklist the corresponding kernel module as suggested in this example. I think you cannot make these changes to Chrome OS by default, I have found no stateful partition in the output of mount that would let me make such changes so you have to do it in chroot.
