Well, I'd say it's fairly simple without edition of views or "abusing and messing with" a cart module:
(EDITED to reflect the correct aliases!)
1. If you have not yet, you should create a (hidden) Joomla menu item for the checkout page e.g. with the alias "checkout".
2. In the Joomla module manager, create a new custom HTML module at a position where you want the button, e.g. below the main content, or in a sidebar like now.
3. By using the "Code Mirror" editor, create the content of the module like this:
<a class="uk-button uk-button-primary" href="checkout (or your alias/link to checkout page)">Proceed to Checkout</a>
4. Add other content, e.g. a "Continue Shopping" button, as you see need.
5. Add CSS, in-line or in custom.css, as you like.
Done?!