I had the same problem, and came to this forum looking for an answer. I found one, albeit in a different way. I also know this answer comes late, but it might help others. I don't think this should make a difference, but just in case, I'm using DVI to HDMI from my PC to my Yamaha receiver. This is the one I wanted to disable the display on, but keep the sound. I use an HDMI cable from my computer to my 4k monitor (different resolution than OP, but still same problem). I'm also using windows 10.
Go into Nvidia Control Panel and duplicate the displays. This will inherently force your 4k into a 1080p/i resolution, and grey out all other resolution options. Close Nvidia. Right click on desktop, go to Display Settings. It'll show the cloned displays. Here, you can change the resolution to 4k, and it'll force the Yamaha (or whatever sound device hopefully) to match the primary monitors resolution.
Using this method, you can keep your high resolution display cloned with a lower resolution display (which is primary for audio), without having to worry about a mini extended display. Of course this only works when you have one monitor or multiple monitors used as clone, although it might still work even if you have one extended and one cloned, I don't see why it wouldn't. Hope this helps some people.