First, welcome!
It is my understanding that your method would work just fine. Map the existing GUID’s to the appropriate field you wish them to live in, and then upload as normal through the Workbench. Specify automatically generates GUID’s in the following tables when one is not provided, but this does not overwrite existing fields.
As to whether you should keep the existing GUID’s or assign a new one for your institution, I would suggest this paper from GBIF. Specifically it mentions the following on page 2:
Should I create a new Persistent Identifier for something that already has one?
If a Persistent Identifier already exists for an object you want to reference, it is generally
better to re-use that existing identifier, rather than generate a new one. However,
whenever a service adds new information, or in some way changes the content or meaning
of the object represented by an existing identifier, it is sometimes useful to assign a new
identifier (in such cases, it is best to refer back to the existing identifier within the
information associated with the new identifier).