In most cases, it's easiest to just use a new Sku for every package. Although if it's easier for you to keep track of your Products by using one Sku for you packages, it is possible.
Reusing a Sku
During the transfer stage, you'll still want to generate a random Sku.
Then place the new Package with the random Sku On Hold until the Original Package is sold out.
Once the Original Package is sold out, Finish the Package.
Now that the Original Package has been sold out and Finished, you can now Release Package Hold on the New Package.
Now copy the Original Sku and then click Edit under your New Package you just took off hold.
Paste in the Original Sku on the Edit Package Page and make sure to click save.
Sku Already Exists
The reason you are seeing this is because the Sku you are trying to use is from a Package that is still Active. Before you can reuse a Sku, make sure it had been Finished.