Sounds like you just need to make another widget of your own in a plugin. So copy the complete code from the default widgets file, and change the class name, then just edit the code you’d like to edit.
class YOUR NEW WIDGET NAME extends WP_Widget {
// ...
foreach ( (array) $comments as $comment) {
$output .= '<li class="recentcomments">' . /* translators: comments widget: 1: comment author, 2: post link */ sprintf(_x('%1$s on %2$s', 'widgets'), get_comment_author_link(), '<a href="' . esc_url( get_comment_link($comment->comment_ID) ) . '">' . get_the_title($comment->comment_post_ID) . '</a>') . '</li>';
}
// ...
}
Then you just register the new widget:
add_action( 'widgets_init', 'register_my_widget' );
function register_my_widget() {
register_widget ( YOUR NEW WIDGET NAME );
}
All that should probably go inside a plugin so you don’t loose your widget when changing themes.
More info:
http://xavisys.com/wordpress-widget/