So I was able to find, install and run the keymap editor, and edit keys. I found a key called "aspect ratio", and one called "subtitle cycle". The problem, though, is trying to get the Shield remote buttons mapped to any keys, and this is, I think, more of a Shield problem than a Kodi problem. I have a 2017 Shield, but a 2019 remote--the one with the Netflix button. In times past, I'm sure the Shield settings contained a way to edit that Netflix button, but now I just can't find it. (I think, perhaps, according to the Shield forums, that that setting has been removed--but since I don't allow my Shield to update, I don't know how it could have been removed from my box.)
However, the 2019 Shield remote does have a "Menu" button, and the Shield settings have a way to edit that button. There are actually three different settings: "Menu short press", "Menu hold", and "Menu double press". For each one of those three, there is a list of actions from which one action be applied to that setting. Most of those actions have to do with functions on the Shield, but there are two actions that sound like they could send something to Kodi: "Send Menu short press to app" and "Send Menu double press to app", but no "Send Menu hold to app". [This is all from memory, from testing last night, so the names may be slightly off, and it may be that "Send short" and "Send hold" are the ones available, and "Send double" not available; but in any case there are two of the three available.] And I couldn't find anything else in Shield settings that would allow to change any other buttons, which all of course have their assigned function on the Shield, and so aren't useful to control Kodi. Just to let you know, when the "short" button was mapped, the "aspect ratio" function in keymap editor showed a five-digit decimal number; when the other button, "hold or double" was mapped, "aspect ratio" showed a longer decimal number--I didn't count, but think it may have been eight digits.
So I was able to apply either of those two button presses to the "aspect ratio" function in keymap editor. But, when playing a video, the "Menu short" button press when mapped, simply caused the OSD to come up, and pressing it again caused the OSD to go away. The "Menu double press" button, when mapped, simply caused the OSD to come up and then immediately go away. At no time did anything happen with regard to aspect ratio.
Now, I'm completely willing to try editing more Kodi files, but I don't know which files to edit, or what changes to make. And, I'm not sure what's even possible, given the limited output of the Shield remote.