Hi,
Go in the menu Customers>Emails history in HikaShop and you can check all the emails sent by HikaShop.
If you see the activation email there, then HikaShop has sent the email and the problem is between your hosting email server and your receiver email server (spam protection, etc).
You can turn off the user account activation if you want in the settings of the Joomla user manager.
Otherwise, you'll have to check with your hosting why the email wasn't sent. You can provide them with a copy of the email details from the menu Customers>Emails history.