You should be able to transfer over the external drive pretty much separately from doing the main migration.
The main migration could be using
- A Time Machine backup of the old Mac's startup drive
- A bootable clone backup of the old Mac's startup drive
I would advise against trying to migrate over Wi-Fi.
Once you've got the new Mac set up, you could attach the external drive with the photo library on it.
If these were in a Photos library (as in the Apple Photos application), you could hold down the Option key while launching Photos on the new Mac, to bring up a dialog that would let you select the Photos library on the external drive. You'd normally only need to do this once, unless you were switching between libraries on a regular basis.
Note that the new Mac might decide to upgrade the format of the Photos library. (This has to do with the version of Photos, and would happen whether or not the old library was on an external drive.)