How to assign custom template to specific products in Woocommerce?

If the changes you need are strictly CSS, you can add the category names as classes to the body_class via the body_class filter.

add_filter('body_class','wpa76627_class_names');
function wpa76627_class_names( $classes ) {
    if( is_singular( 'product' ) ):
        global $post;
        foreach( get_the_terms( $post->ID, 'product_cat' ) as $cat )
            // maybe you want to make this more unique, like:
            // $classes[] = 'product-category-' . $cat->slug;
            $classes[] = $cat->slug;
    endif;
    return $classes;
}

This code checks if we are viewing a single product page, then loops over all product_cats, adding the slugs as classes to the body tag. This could also be adapted for any post type or taxonomy.