Custom php page outside the scope of my theme

is this not something that you could put into your functions.php file as a new function, adding the action to init to fire off on the page load? You could then put in an if statement so it only runs when specific criteria is met, such as a page ID or slug or template is loaded?

If this does need to be a blank page, then you could just create a file in the theme root called something like page-processor.php where you could just put in your required data. This page will load as blank so long as you don’t include get_header() or get_footer(). Once you’ve created the file and given the template a name (Take a look here for some page template info if you’re unfamiliar) then you can set that blank template as the page template in the attributes tab.