Hi there,
Editing configuration of the Launch web property will directly take into effect(with no publishing required). Although the "Domain" field is required, the Launch property will work on any domain where it's implemented.
Also, you may add multiple domains to the same property as per your requirement. Hence, as a recommendation rather than deleting the existing domain and replacing it with a new domain, you may directly add a new domain to the list.
Reference document: https://docs.adobe.com/content/help/en/core-services-learn/implementing-in-websites-with-launch/conf...
PS: The main purpose of the domain field is to pre-populate menu options in the Rule builder. For instance: If condition type while creating a rule is "Domain", it will show up all the domains added to the property.
Hope this helps!