Yes, you can copy the vanilla index.html file from C:\Users\<USER>\AppData\Local\Shapespark\app-<VER>\resources\webwalk\ to the scene directory Documents\Shapespark\<SCENE>\. Then, you can adjust scene’s entry index.html file to your needs, including replacing the default play button. Modified index.html is used only in the view mode, it doesn’t work in the scene editor.
Which plan do you have? Customizing index.html is not possible in the Starter plan.