Solution:
The code below will solve that problem. The display of the HTML (drop-down list) can be applied anywhere on the page via template overrides or via the desired hook.
In this answer I have combined both in one
function action_woocommerce_after_single_product_summary() {
// Display drop-down list
echo '<select class="frame">
<option value="">Choose frame</option>
<option value="">Without frame</option>
<option value="20px solid red">Red</option>
<option value="20px solid blue">Blue</option>
<option value="20px solid yellow">Yellow</option>
</select>';
?>
<script>
jQuery(document).ready(function($) {
// On change
$( 'select.frame' ).change( function() {
var changeframe = $(this).children( 'option:selected' ).val();
// DEBUG
console.log(changeframe);
// Add border
$( '.woocommerce-product-gallery__wrapper' ).css( 'border', changeframe );
});
});
</script>
<?php
}
add_action( 'woocommerce_after_single_product_summary', 'action_woocommerce_after_single_product_summary', 10, 0 );