Is it possible to "clone" a disk which contains programs by performing a copy of all the disk contents (preserving file attributes) from source to destination disk, and unplugging the source disk and changing the drive letter of the destination disk to match that of the source?

Context

I have a two disk Windows 8 system with a system drive and a data drive. Recently, the data drive developed a number of bad sectors leading to IO errors. I have been sent a replacement drive so I simply need to clone the contents of this data drive onto the replacement. The drive contents include documents & media, user folders (My Documents and related), and some programs (games etc).

Problem

The problem is that the bad sectors on the source disk causes most disk cloning tools to fail with read errors. Attempted approaches include:

1. Disk clone from live boot environment with Acronis True Image. Fails due to read errors.
2. Disk clone from live boot environment with Clonezilla. Fails due to read errors.
3. Disk clone using Roadkil's Unstoppable Copier. Fails due to hardware timeouts in the HDD (application hangs indefinitely).
4. A straightforward copy from source to destination disk using FreeFileSync (preserving file attributes and metadata). This succeeds.

So at the moment I have a replacement disk which contains all of the data from the original disk. Now all I need to is somehow get Windows to replace all references to the old disk to the new one. Is this possible by simply swapping the assigned drive letters? Any help would be greatly appreciated, thanks!