Send custom 404 error without changing page

[Rt Ibmer]

What is the best way to send a custom 404 error to the browser without it changing the URL on the user?

For instance I currently have this:
  error_page  404         /404.php;

But then the URL in their browser is http://mysite.com/404.php which can be annoying to users because instead of just fixing a typo in the url they now have to retype the url.

So instead what I want to do is show the content from 404.php but have the browser be on the typo url still. 

For example let's say the real page is products.php (products, plural) and they type http://mysite.com/product.php (product, singular).

So now I want their browser to still show http://mysite.com/product.php, but to actually show the 404.php page in the browser.

What is the best way to do this?

This is how I have done it now, but I do not like using the -f check because now I feel like nginx has to check the file system on every request to see if a file exists? That seems very inefficient don't you think?

location ~ .*\.php$ {
  if (!-f $request_filename) { rewrite . /404.php; }
  ... other php and fastcgi stuff here
}

So again, this does work, but I am concerned about the added overhead of the server checking to see if the file exists on each request.

Is there a better way? Ideally I would like to do something like this:

  error_page  404         /404.php noredirect;

where the "noredirect" (which I just made up) would tell Nginx "hey if you ever need to issue a 404 get the content from 404.php but don't redirect them to the page, instead just feed them the content".  Is this possible?

The idea is that same except in this later case only when the server finds a page is missing does the action occur. Whereas in the -f case the server has to check for the file in every request, when 99.9% of the time there will be no 404.

Please let me know your thoughts. Thank you!!