The rest of your site isn't 'attached' to the index page, you can delete it, although the site will not work until you have a new page called index.htm (or .html).
The simplest wat around the problem is just to create your new page and then upload it - you'll be asked if you want to overwrite the existing page.
Without knowing a bit more about the software you're using I can't be more helpful. The problem with simply uploading a new index page is that the navigation links may not work - it all depends on how you've created the page. Post back with more information.