<?php
/**
  *  Couldn't find copy/paste code anywhere so I wrote it myself. The interwebz failed me.
 */

/** The category ID's with the posts you want to change */
$category_ids = array(48, 50, 51, 52, 53); // array of ints or single int

/** The shipping class to set for the products */
$shipping_class_slug = "postcards"; // found in "shipping classes" in woocommerce settings

/** Run query to collect our data */
$products = new WP_Query(array(
    'post_type' => 'product',
    'posts_per_page' => -1,
    'fields' => 'ids',
    'tax_query' => array(
        array(
            'taxonomy' => 'product_cat',
            'field' => 'term_id',
            'terms' => $category_ids,
            'operator' => 'IN'
        )
    )
));

/** Set our shipping class on each product */
foreach ($products->posts as $pid) {
    wp_set_object_terms($pid, $shipping_class_slug, 'product_shipping_class');
}

/** reset the query */
wp_reset_query();