How do I toggle pagination on/off in search results and category listings via a link?

I think it should work by hooking into pre_get_posts:

function wpse_254661_remove_pagination( $query ) {
    if ( $query->is_main_query() &&  get_query_var( 'onepageprint', 0 ) ) {
        $query->query_vars['nopaging'] = 1;
        $query->query_vars['posts_per_page'] = -1;
    }
}
add_action( 'pre_get_posts', 'wpse_254661_remove_pagination' );

Like this you can modify your query right before it gets fetched and the query object gets passed by the hook right into the function. There is also a check to only affect the main query.