How to handle updates that aren't appropriate for Server Core editions?

My suggestion is:

• Move the Core Servers into their own Computer Group in WSUS
• Decline any updates not appropriate for that Server edition (e.g. Silverlight!) (Well, Silverlight actually does not belong on a server at all - other story)
• WSUS only does what you tell it to do - you approved Silverlight for the Server (or at least you did not decline it)

This should get you started.
I have installed KB2919355 sucessfully on a Server Core installation.

You can't decline an update for one computer group, as far as I can tell: you can only not approve it. A not-approved update still shows up as failed or needed.