I had exactly the same issue with MyCloud EX2 (the latest firmware) - the Samba shares could not be accessed when my router’s WAN connection was down. Similarly to OP I don’t use any cloud features.
The cause of the issue is the configuration of the Samba server on MyCloud which for god-knows-what reason needs an accessible DNS server to work. So here’s what I did:
I set MyCloud to use my router as the DNS server via static IPv4 configuration - so if your router has IP address 192.168.1.1, just enter 192.168.1.1 in the DNS field. After making this little change the Samba shares could be accessed even without the Internet connectivity - although opening them takes a bit longer (probably because of some DNS timeouts).
This solution may or may not work for you depending on whether your router can act as the local DNS server.
Hope this helps if anyone else encounters this frustrating issue ignored by WD.
