As Nicolas said, you could create a new Joomla menu item of the type "HikaShop user registration". Just like any other Joomla menu item, you may add it to an existing menu. Or you could use a "hidden", unpublished menu, so you have a link which you could use for e.g. the button you mentioned, which you may want to place separately somewhere on your site.
You would then have a page with the registration form. To add the login, you could create a Joomla module of the type "Login" and assign it to the registration menu item, so it shows up on that page. Which module position you want to publish it to depends on your taste and template, but if you want it to look somewhat similar to the checkout, you may try to place it in a sidebar, preferably on the left.
If you're having further difficulties with it, it's recommended to study Joomla more, e.g. via some of the many tutorials on-line, because all of this is general Joomla procedure and not related to or depending on HikaShop.