Just downloaded TechTool 10 and I'm wondering if I need to remove and rebuild the existing eDrive. I've also upgraded to High Sierra recently.

To get an eDrive with TechTool Pro 10 and High Sierra on it, install TechTool Pro 10, remove the present eDrive, and then make a new eDrive.

Be sure to make a backup of all of the volumes (except the eDrive) that are on the device that contains the eDrive before you begin. Creating or removing an eDrive involves writing to the partition map of the device, something that has always triggered a backup warning from Apple.