I would recommend scenario 1 you mentioned above.
Serveral ways can meet your requirement like below
- Standing up a new 2013 server, move mailboxes.
- Creating a DAG, add 2nd server, seed DB's, make DB's active on new server, remove DB's from first server, decommission first server. (You could ignore this since you don't want to create DAG)
If you choose scenario 1 to 'replace' your old server, this article should be helpful to you: Performing a Like for Like Exchange Server Migration, it introduces about some details we need to pay attention to (contains your concerns above) .
Mainly steps list
1.Install the new Exchange server
2.Configure the new Exchange server
- Client access (Outlook, OWA, mobile devices, etc)
- Transport (mail flow)
- Mailbox databases
3.Migrate data and services to the new Exchange server
- Client access
- Transport services
- Mailboxes
4.Decommission the old server
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