That's what I was saying about Javascript processing: You can make the arrow keys work, but it will take added code. (And I am not the right one to do that kind of stuff, as Javascript is definitely not my strong suit. But I've mucked some stuff together over the years using the advice of others here and some web searching.)
As an example, my The Decision Maker macro uses a custom HMTL prompt and key processing to react to key presses in the web view.
I imagine someone much better than I at Javascript could explain how to code support for moving and selecting with the arrow keys in an HTML prompt.
The list portion of the box never gets focus; it's always on the search box. However, the arrow keys (up and down) and the Enter key should work anyway—they do in my testing here.
-rob.