Update:
Not sure if this is the best way to do this but here’s what I did.
I went to this file:
includes\templates\template_default\templates\ tpl_shopping_cart_default.php

and I changed the code in line 132:

<div class="buttonRow forward"><?php echo '<a href="' . zen_href_link(FILENAME_CHECKOUT_SHIPPING, '', 'SSL') . '">' . zen_image_button(BUTTON_IMAGE_CHECKOUT, BUTTON_CHECKOUT_ALT) . '</a>'; ?></div>

change to this:

<div class="buttonRow forward"><?php echo '<a href="' . zen_href_link(FILENAME_NO_ACCOUNT, '', 'SSL') . '">' . zen_image_button(BUTTON_IMAGE_CHECKOUT, BUTTON_CHECKOUT_ALT) . '</a>'; ?></div>

Notice the change from “FILENAME_CHECKOUT_SHIPPING” to “FILENAME_NO_ACCOUNT” – this takes the user right to the no account sign up page used in COWOA.