Remove "Default Template" from Page Editor choices

I am working on a theme that will be used like a cms with only page templates.

The theme does not use index.php, but I have to keep a copy (blank with no code) with my other files because WP requires it for all themes.

So when I’m in the page editor and go to select a template, the first choices is always “Default Template” which represents index.php.

How can I remove it from the drop-down list. Being an empty file, it will cause problems if accidentally selected.