Start by removig the display of the button:
In a copy of this file placed in /your template /templates folder
tpl_shopping_cart_default.php
find and remove the red code check and see if it did not break anything if it did just delete your copy
Code:
<!--bof shopping cart buttons-->
<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>
<div class="buttonRow back"><?php echo zen_back_link() . zen_image_button(BUTTON_IMAGE_CONTINUE_SHOPPING, BUTTON_CONTINUE_SHOPPING_ALT) . '</a>'; ?></div>
<?php
// show update cart button
if (SHOW_SHOPPING_CART_UPDATE == 2 or SHOW_SHOPPING_CART_UPDATE == 3) {
?>
<div class="buttonRow back"><?php echo zen_image_submit(ICON_IMAGE_UPDATE, ICON_UPDATE_ALT); ?></div>
<?php
} else { // don't show update button below cart
?>
<?php
} // show checkout button
?>
<!--eof shopping cart buttons-->