Your website seems to be well configured since the beginning, actually there is no registrations on your website, only the addresses are asked to the customer.
Nicolas was right, you just have to replace the text like he explain it to you (7 post ago).
If you replace the translations for "Login or create a new account" and "Register" by "", and replace the text on the "Register" button by, for example, "Validate address", so you will see that there is no registration and only the address is asked.
nicolas wrote: What you want is to change the text written there.
Like any text in HikaShop's interface, you can modify these texts with translation overrides as explained there:
www.hikashop.com/en/download/languages.html#modify