Every scenario involving directory synchronization requires you to make changes to synchronized users and their properties on-premises. This is not specific to Exchange and disabling/removing the Exchange bits do not change things - the objects will still need to be managed on-premises, until you disable synchronization.
Now, for the specific query on updating proxyaddresses, there is a workaround you might be able to use. In a nutshell, run the following cmdlet:
Set-Mailbox ******@domain.com -WindowsEmailAddress ******@domain.com
This will add ******@domain.com as the primary SMTP address for the user, while preserving existing aliases. Keep in mind that changes might be overwritten during a full sync cycle, so in the long run, you should consider removing the sync altogether.