Share a Custom Taxonomy among different Custom Post Types

Hallo!
I would like to associate different Custom Post Types to a same Custom Taxonomy. And I’m looking for the best way to do it. I explain better.

I’ve two Custom Post Types: Sculptures and Sketches.
I’ve two Custom Taxonomy: Projects and Materials.

Now, the Projects and Materials are associated with Sculptures, that’s the way I organize Sculptures in Projects and depending of the materials they’re done.

The Sketches are related to Projects, the Sculptures are single object born inside a Project.

No problem in creating the Custom Taxonomies and Custom Post Types. But, in the Dashboard I can display Projects and Materials only for Sculptures, or only for Sketches.

Then I can display columns to better visualize Sculptures and Sketches, and I verified that Projects and Materials appear now for every Post Type, even the default. I guess I could do for Pages, too, I got it.

Here the code I’m going to use to visualize those column only where necessary. Please, amend it if you deem it dangerous or not optimal. Thanks!

// Registering the columns for Post Types
add_filter( 'manage_posts_columns', 'custom_columns' );
function custom_columns($defaults) {
	if ( 'sculpture' == get_post_type() || 'sketch' == get_post_type() ) {
		$defaults['project']	= __('Projects');
	}
	if ( 'sculpture' == get_post_type() ) {
		$defaults['material']	= __('Materials');
	}
	// for all Post Types
	$defaults['featured']	= __('Featured'); // this's shared among all Post Types
	return $defaults;
}

This way I display the Projects column only for Sculptures and Sketches; The Materials column only for Sculptures; and the Featured column for every types of Post.

Then, the code to actually make the columns work.

// Actually adds the columns where necessary
add_action('manage_posts_custom_column', 'taxonomy_custom_columns', 10, 2);
function taxonomy_custom_columns($column_name, $post_id) {
	global $wpdb;
	global $post;
	if ( $column_name == 'project' ) { // name of the taxonomy
		$tags = get_the_terms($post->ID, 'project');
		if ( !empty( $tags ) ) {
			$out = array();
			foreach ( $tags as $c ) {
				$out[] = "<a href='edit.php?post_type=".get_post_type()."&project=$c->slug'> " . esc_html(sanitize_term_field('name', $c->name, $c->term_id, 'project', 'display')) . "</a>";
				echo join( ', ', $out );
			}
		} else {
			_e('Not associated with any Projects'); // No Taxonomy term defined
		}
	} else if ( $column_name == 'material' ) {
		$tags = get_the_terms($post->ID, 'material');
		if ( !empty( $tags ) ) {
			$out = array();
			foreach ( $tags as $c ) {
				$out[] = "<a href='edit.php?post_type=".get_post_type()."&".$column_name."=$c->slug'> " . esc_html(sanitize_term_field('name', $c->name, $c->term_id, $column_name, 'display')) . "</a>";
				echo join( ', ', $out );
			}
		} else {
			_e('No Related Materials');
		}
	} else if ( $column_name == 'featured' ) {
		$featured_checkbox = get_post_meta($post->ID, 'featured_checkbox', true);
		if ( !empty( $featured_checkbox ) ) {
			$output = '<a href="https://localhost:8888/mariakosh/wp-admin/post.php?post='.$post->ID.'&action=edit">';
			$output .= 'Featured';
			$output .= '</a>';
			print $output;
		} else {
			_e('');
		}
	} else {
		echo '<i>'.__('None').'</i>'; // Only 2 columns, blank now.
	}
}

And till here, everything seems to work just fine.

Now, to have the Custom Taxonomy Project also for Sketches, I would encapsulate the relative code between something like

if ( 'sketch' == get_post_type() ) {

But my doubt is about this lines:

register_taxonomy(
	'project', // The name of the custom taxonomy
	array( 'sculpture' )
)

Can I modify it in…

register_taxonomy(
	'project', // The name of the custom taxonomy
	array( 'sculpture', 'sketch' )
)

…without messing everything up?

Thanks for reading a so long text!!
Carlo