If you imaged the entire drive when you created your backup, all your drivers should be included in that image.
I can boot a Win 8 laptop with a Seagate DiscWizard Rescue CD that was created on my Win XP desktop. I do have to change BIOS from UEFI mode to Legacy mode to boot from any CD in the lappy, and you may need to do that on your XPS too.
When it gets to the first screen, DiscWizard asks if I want to boot Windows or run DiscWizard. I choose DiscWizard, and it loads but then says it can't find any Seagate drives (my lappy has Toshiba HDD) so it exits. But you won't have that problem when you use the Rescue CD to boot up the XPS which will have a new Seagate drive.
So if your lappy has a Seagate drive, you should be able to install DiscWizard and create the Rescue CD. Or, find another system with a Seagate drive, install DiscWizard and make a Rescue CD. Then use it to boot the XPS. After you restore the image to the new drive, you'll have to change BIOS back to UEFI mode or it won't boot from the hard drive.
It's worth a try and doesn't cost much more than the price of the blank CD. Besides, I don't know if DiscWizard will even detect the Seagate drive in a USB housing. So what you're planning may not work either.
