Changing taxonomy term by slug (wp_update_term)

As you hinted in your question, you could use get_term_by() to return an object or array containing the term’s id, then use it to update that term. Something like this should work:

$your_term = get_term_by( 'slug', 'your_slug', 'your_taxonomy' );

if ( false !== $your_term ) {
    wp_update_term( $your_term->term_id, 'your_taxonomy', $args );
}

References:

http://codex.wordpress.org/Function_Reference/get_term_by

http://codex.wordpress.org/Function_Reference/wp_update_term