There are two options here. The easiest one is to not put a sign up link on the website, but have a "request membership" sign up form. You could use the contact page for that if you wanted.
Then you get an email when they fill that out. You would create the account (just copy and paste the info) and email them an invitation. They click the link in the invite to make the password.
The other way is let them create the account, but hide the pages with the Locksmith app. Then after you approve them you would apply a "tag" to the customer account so they can see the pages and products locked with Locksmith.