How to register a new user via hidden form on the side

We would like to send new users the link to register in the website.
But this link should only be visible for the user, and should not be published on the site and it should be hidden for search engines.
The new user should fill the form and fill in the usual fields.
Once the form has been submitted, then it should be reviewed and approved by a moderator.
We have SEF enabled on our site.

How can we best do this ?

Disable the registration link in your CB Login module then give users the below URL structure for direct registration page access.

YOUR_DOMAIN_HERE/index.php?option=com_comprofiler&task=registers

You can also enable moderator registration approval within CB > Configuration > Registration.

You however may want to make the whole process more secure and easier by using CB Invites then marking the Invite Code field as Required. This means the user would need to explicitly be sent an invite, which contains an invite code in order to register. If they don't have a valid invite code then registration is rejected. This prevents security issues of someone discovering your registration URL or a user handing it out to others. Your moderators would be able to easily invite users from their Invites tab on their profile. They can also monitor if/when the invite is accepted.

I used the link as proposed above but get the message that I should be authorized to watch the page. The CB Login module is public.

I installed the CB invite plugin and first impression is great, thanks.
However When I use the link in it or the link described above then I am landing on a site saying I am not allowed to access it.

SEF is likely using the first CB menu link it finds, which is probably not publicly accessible. Ensure you've a public and published Joomla menu link to CBs profile page. This like is mandatory, but the menu module it's on does not need to be enabled. It's simply needed for its Itemid.