search and replace when changing to a second-level domain

Hi there,
wondering what is the best way to make a change for a second level domain, that is effectively adding to the same search value. For example changing from example.com to example.com.au ?
Search and replace for https://example.com to https://example.com.au would result in https://example.com.au.au, if https://example.com.au already existed in the database, for example in ‘siteurl’ and ‘home’ if already changed on importing a database.
Would the safest option be to define the siteurl and home in wp-config.php, and then do a search for https://example.com and replace to something else like https://example2.com, and then do a second search and replace this time for https://example2.com to replace with https://example.com.au ?
Does that make sense ? Or is there an easier / safer way ?