After three attempts that ended with an error immediately after entering the personalization information, I contacted Alsoft Technical Support from their website. Below the answer by Alsoft. Worked fine for me. When the error message appeared (and before dismissing the message), I copied the disk image file from the /private/tmp/ folder and burned it with Disk Utility.

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Generally, this type of error indicates that something other process/
application is interfering with the updater (even though you have
started the computer in Safe Mode).

You can try burning the disk image manually using Disk Utility under OS
X 10.3.x or higher.

The updated DiskWarrior disk image is in the /private/tmp folder on the
hard drive.

To find the .dmg file do the following.

1. Run the updater.  Allow it to read your DiskWarrior 4.x disc and
enter the registration information when requested.

2. When it asks for a blank disc, go to the Finder (i.e. click on the
desktop).

3. In the Finder, select the "Go to Folder..." command located in the
"Go" menu.

4. The Go to Folder dialog will open and you will need to type the path
"/private/tmp" (do not type the quote marks) and then press Go.

This will open the tmp folder and you can then copy the .dmg file to the
desktop (see note below).  When dragging and dropping the disk image
file from the tmp folder to the Desktop, make sure you hold down the
"option" key so that a copy will be made instead of moving the
original.  Then burn it using Disk Utility (i.e. Use the "Burn" command
from the "Images" menu and select the .dmg file).

NOTE:
The .dmg file is deleted when the updater quits.  You need to make a
copy of this temporary file before quitting the updater so that it does
not go away.