Migrating to Azure Files - Best Cutover Strategy

Hi All,

Looking for some help regarding a cutover strategy for an on prem file server to Azure Files migration.

I have experience with the setup of Azure Files- creating the Storage Account, joining it to AD, copying the files and permissions over via Robocopy, etc.  

My question is based on the cutover strategy so it's least disruptive to users.  We currently DO NOT use DFS namespaces on prem - so I'm not able to just repoint the DFS names to the new Azure Files location.  Many users have shortcuts to files that would be affected after the cutover, especially since we're not using DFS.

What is the recommended approach for this scenario?  
Would a CNAME redirect work in our local DNS?

Would implementing DFS on prem first solve anything, or would the end users need to know the new DFS path anyway?
Again, the goal is to be as least disruptive as possible.  Wish we had DFS implemented, it would be a simpler approach.

Thanks for your suggestions.