Changing Storage for Cluster Resources

We have a Windows Server 2008 R2 Cluster set up that hosts SQL Services. We need to move the backend storage for the SQL Data/Log Drives to another storage. Can I -

1. Shut down SQL (Drives:F,G) and Cluster services
2. Make new storage available with NEW Drive letters H, I
3. Copy all files from Drives F,G to Drives H,I
4. Rename old Drives F,G to R,S (essentially discard)
5. Rename new Drives H,I to F,G (original drive names)
6. Restart SQL and Cluster services

In other words, do SQL and the Cluster service operate purely on the Drive Letter where this might work? Or does it use some identifier behind the scenes which would cause the cluster to break inspite of the new Drives having the same Drive Letter?

If it will break, is there another way to do this?

Thanks in advance,
Jake.