To do what you want without a plugin (there are plenty of plugins that exist solely to provide a back-to-top button) you will need to do one of the following …
1) Inject the HTML / JavaScript using the functions.php for the button using wp_footer hook into functions.php and add CSS to style it
2) Create a child theme to incorporate the above
If you choose option (1) then you will have to modify the theme which will prevent you from being able to update the theme without re-applying your changes which is worse than the small speed decrease a plugin may cause.
If you choose option (2) then you will be using a child theme (which may not be compatible with future versions of the parent theme) and will slow your site down (maybe more than using a plugin).
So I would probably just use a plugin.
Oliver