If there isn't a switch on the Shipping Estimator to remove the totals but you can customize the template tpl_modules_shipping_estimator.php in your templates and overrides and comment out the display for:
Code:
<?php if (!empty($totalsDisplay)) { ?>
<div class="cartTotalsDisplay important"><?php echo $totalsDisplay; ?></div>
<?php } ?>
and below that for:
Code:
<?php if (!empty($totalsDisplay)) { ?>
<div class="cartTotalsDisplay important"><?php echo $totalsDisplay; ?></div>
<?php } ?>
But first try the switch in the Configuration ... Layout Settings ...
Shopping Cart - Show Totals
Show Totals Above Shopping Cart?
0= off
1= on: Items Weight Amount
2= on: Items Weight Amount, but no weight when 0
3= on: Items Amount
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