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What happens if you hook up the phone to a computer via the data cable?
I use the s8 and a MacBook Air so use Android Transfer that lets me have complete access to the phones files.
I've not used Samsung's Smart Switch but it maybe an option to try too.
If the phone works (apart form the screen), can you get acces to a PC and view the phone as external storage in Windows Explorer? It's possible that might not require you press accept (I don't know whether that's a requirement of Android Transfer or Samsung). I also don't know whether the Mac file manager has a similar option?
First way, you can use a Samsung smart switch tool, it can enable transfer data between Samsung phones.
Second way, you can plug your old phone into computer, then backup the data on computer, and then move the data to the new phone..
Third way, you can use a MobiKin mobile transfer software, it is also possible.