Deleting files from an existing ZIP file is not currently available from the built-in ZIP action. We expected users would always create the ZIP file from scratch in an automated situation, but we'll put that on the list as an enhancement request. For now you could use a Run Program action to invoke WinZip's command-line interface [1] to automate deleting from the ZIP file.
[1]
http://www.winzip.com/prodpagecl.htm