Well, I wasn't able to combine them, but I found the following section in show_block_cart:
<?php
}
if(!empty($this->options['show_price']) && !empty($cart->coupon) && !empty($this->options['show_coupon'])) {
?>
<tr>
<td colspan="<?php echo $row_count - 2; ?>" class="hikashop_cart_empty_footer"></td>
<td id="hikashop_checkout_cart_coupon_title" class="hikashop_cart_coupon_title hikashop_cart_title"><?php
echo JText::_('HIKASHOP_COUPON');
?></td>
<td class="hikashop_cart_coupon_value" data-title="<?php echo JText::_('HIKASHOP_COUPON'); ?>">
<span class="hikashop_checkout_cart_coupon"><?php
if(empty($this->options['price_with_tax']))
echo $this->currencyClass->format(@$cart->coupon->discount_value_without_tax * -1, @$cart->coupon->discount_currency_id);
else
echo $this->currencyClass->format(@$cart->coupon->discount_value * -1, @$cart->coupon->discount_currency_id);
?></span>
</td>
</tr>
which I moved below the shipping section it proceeded. Worked!!
I also overwrote the HIKASHOP_COUPON and HIKASHOP_CHECKOUT_COUPON constants in my language overrides.