Moving an existing wpmu network blog to new domain

Hi,
I have a development blog under the wpmu network - currently as a subdomain (blog.maindomain.com)
This blog is now finished and should work on its "real" domain (www.blogdomain.com).
Can you give me a hint how to proceed?

- Change blog URL in settings of blog.maindomain.com to http://www.blogdomain.com
- Change Domain in Domain Mapping
- Replace blog.maindomain.com with http://www.blogdomain.com with a tool like https://interconnectit.com/products/search-and-replace-for-wordpress-databases/

Is this correct?

Thanks!