Hi @S_NO ,
If you want to use the same IP and minimize downtime, just like you said, do a fresh backup, you can see this thread:
https://social.msdn.microsoft.com/forums/sqlserver/en-US/e614defb-f996-437b-a4bd-2f521a1ead36/db-mirroring-migration-to-a-new-sql-server-hardware
For example,
You may try for principal server create the mirror database, data sync and failover
Specify a Server Network Address (Database Mirroring)
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