Unfortunately, you will not be able to hard code something in the index.html file because of the problems you previously mentioned but instead, you will have to modify the JavaScript to make sure these buttons are only displayed with their corresponding maps. At the beginning of the map load function in the JavaScript, there is a line that append's a map's specific description to the description-pane. Later in the change map function, the app will toggle the visibility of the different descriptions.
One way to accomplish this would be to append the new buttons within a map's specific description, then you will not have to worry about having the buttons appear all the time.
Once you have that, you will need to write a new function in the JavaScript to apply an action when someone clicks on these buttons. This is where you can use the map.getLayer("layer-id").hide() or map.getLayer("layer-id").show() methods.