Since you want to update Checkout
word to Order Now
ONLY in the Header Cart => Mini Cart, do the following:
Assuming you are using the RWD theme, navigate to app/design/frontend/rwd/default/template/checkout/cart/minicart/items.phtml
Line no: 94 & 95 From:
<a title="<?php echo $this->quoteEscape($this->__('Checkout')) ?>" class="button checkout-button" href="<?php echo $this->getCheckoutUrl() ?>">
<?php echo $this->__('Checkout') ?>
</a>
Update to:
<a title="<?php echo $this->quoteEscape($this->__('Order Now')) ?>" class="button checkout-button" href="<?php echo $this->getCheckoutUrl() ?>">
<?php echo $this->__('Order Now') ?>
</a>
Screenshot:
Let me know if this helps.
Happy Coding...