Is there a way I can use non-post content in this plugin?

Yes. You can use one of build-in filters:

To replace whole box:

add_filter( 'iworks_upprev_box', 'iworks_upprev_box_mycontent' );
function iworks_upprev_box_mycontent( $content )
    $value = '<div id="upprev_box">';
    $value .= '<h6>My own title</h6>';
    $value .= '<div class="upprev_excerpt">';
    $value .= '<h5>Lorem ipsum</h5>';
    $value .= '<p>Lorem ipsum dolor sit amet, consectetur ';
    $value .= 'adipiscing elit. Vestibulum auctor neque vitae orci ';
    $value .= 'ornare et vehicula eros molestie.</p>';
    $value .= '</div>';
    $value .= sprintf(
        '<a id="upprev_close" href="#" rel="close">%s</a>',
        __('Close', 'upprev')
    $value .= '</div>';
    return $value;

Get code:

Where to put this code?

There are three ways:

  1. made a one-file-plugin and put file into wp-content/plugins, then turn it on
  2. made a one-file-plugin and put file into wp-content/mu-plugins
  3. put this code into functions.php in current theme

I recommend using option 1 or 2, but 3 is the easiest.