Move your content to a new Mac without using migration assistant.

Export all your data to an external drive Then copy it into the same locations on your new computer. I don’t know how you would do mail that way, but if it’s an IMAP account everything is on the server. Anything you move to an on my Mac mailbox would need to be exported from mail and then imported into the new mail program on the new computer. It’s really rather a pain to do it manually.

After the new Mac is installed & running, you could enable sharing, then via your WiFi or ethernet network log your old Mac into your new Mac and use the Finder to copy folders & files to the new Mac.

Or, if both Macs have Thunderbolt ports you could set up a Thunderbolt connection between them. Here's a video that shows how to do it. (BTW, it does not have to be TB3, any flavor of Thunderbolt will work but you may need the Apple Thunderbolt 2-to-Thunderbolt 2 adapter if your old Mac has TB2 but your new Mac has TB3.)

Note: this is only for moving data. You cannot move user accounts or applications this way.