Ryan's suggestion was the right one. It's easy to use hook_form_alter() to remove the update button, add an empty cart button, then handle the empty cart button press in your own submission function - all without modifying core.
In your own module "example_module", add this code:
function example_module_form_alter($form_id, &$form) {
if ($form_id == 'uc_cart_view_form') {
// Remove "Update button" from form
unset($form['update']);
// Add "Empty cart" button to form
$form['empty'] = array(
'#type' => 'submit',
'#value' => t('Empty cart'),
);
// Add new submit handler for the "Empty cart" button,
// then call the default submit handler to deal with the
// rest of the form
$form['#submit'] = array(
'example_module_cart_view_form_submit' => NULL,
'uc_cart_view_form_submit' => NULL,
);
}
}
function example_module_cart_view_form_submit($form_id, $form_values) {
switch ($form_values['op']) {
case t('Empty cart'):
// Take action to empty the cart
uc_cart_empty(uc_cart_get_id());
drupal_set_message(t('Cart is now empty...'));
return 'cart'; // set redirect
}
}