How to not load stylesheet and how to load a second stylesheet on a page

There are a few ways to do this depending on your preferred approach and the current theme you are working in.

The “WordPress Way” would be to enqueue the new style sheet in functions.php using wp_enqueue_style()

https://codex.wordpress.org/Function_Reference/wp_enqueue_style

You can remove the reference to the original stylesheet by deleting the reference to it in your existing theme. Depending on the theme the style sheet may be loaded directly in header.php or enqueued elsewhere, perhaps in functions.php (really depends on the theme).

If you still can’t find it you can try to dequeue it in functions.php using wp_dequeue_style()

https://codex.wordpress.org/Function_Reference/wp_dequeue_style

If all else fails a last resort might be to delete the styles from that style sheet and replace them with new ones. Just be sure not to delete the comments at the top of style.css as WordPress relies on those notes for important theme details.