I've moved this to our Risk & Compliance area for better visibility by a product expert.
The entry you need is located in the Configuration table of the Hercules SQL database (named servername_Hercules). In the 'PropertyName' column of that table, locate the 'ServerGlobal.ServerGuid' value. Just to the right is a value in the 'PropertyValue' column. This long string is the Server GUID. This is the only value you need to preserve when moving the Hercules server to another server, or if re-installing everything on the same server.