Alternately, there are some other shelves of a more normal height that I could just set it on top of; the power cable would be much less visible that way.
But I do like the idea of having it on a wall. As you say, the trick is going to be working out how to camouflage the cable.
I don't know if you've tried and hated it or not, but spackling is surprisingly easy, and most landlords will provide you with matching paint (either free or at cost, depending on your landlord and probably the amount you need). You can patch probably a dozen holes in an hour (only counting active time, not time spent drying) including painting.
It's not fun, but I've resorted to it because spackling nail holes is extremely easy compared to fixing the carnage left behind when one of those "won't mess up your wall" patches doesn't come off cleanly.
It's also worth checking whether "normal wear and tear" is the tenant's responsibility or the landlord's responsibility in your jurisdiction. When I was in SF and looked, it seemed to be largely on the landlord, so they were not allowed to charge for repairing holes considered "normal wear and tear" (which hanging pictures and the like generally was). My readings said the only time you were responsible for them is if there were an excessive number (though excessive wasn't quantified).
https://www.cableorganizer.com/p/taperwire-flat-speaker-cabl...
We need super-long-life batteries. One day ...
It's doable today, just not convenient.