Benjamin,
There are many ways of compressing data. The data compressed with Zlib is not compatible with WinZip. If you need to create files which can be opened using Winzip you'll need to take another approach. I've personally had luck with calling the Winzip command line interface from LV (there are some examples in the development library that use the Winzip command line). You need to install a seperate add-on to get command line support for winzip:
http://www.winzip.com/prodpagecl.htm
Alternately, you could try one of the older command line compression programs such as pkzip. Winzip should open archives created with those programs. You could also search around to see if you can find an ActiveX compression utility that supports one of the winzip compression schemes.
Regards,
Ryan K.