I don't know about Workflow Manager, but this can be done via the Platform Service (if that is what you mean by "web service").
POST to the DocuWare resource:
The post data (XML) looks like this to clear out all keywords for a field:
<?xml version="1.0" encoding="utf-8"?>
<?xml-stylesheet type="text/xsl" href="/DocuWare/Platform/Content/standard.xslt"?>
<DocumentIndexFields xmlns:s="http://dev.docuware.com/schema/public/services" xmlns="http://dev.docuware.com/schema/public/services/platform">
I just tested the non-.NET routine I wrote to do this and was able to add, modify, and clear out keywords no problem. I imagine in .NET you simply pass an empty keywords List (or "null"?) to whatever method wraps the SDK resource.
Hope this helps, if using the SDK is an option.