There is no need to convert .zip files, they are platform independent.
A .zip file created in a Windows or Linux environment using WinZip or other similar applications, will open just fine on Mac OS X, unless you used some special features, that are WinZip dependent.
Mac OS X has a .zip unarchiving package built in, but you can also use The Unarchiver to unzip files on Mac OS X.
Wow, WinZip is at version fourteen, some years ago they were still at eight, and that for several years, like Winamp was version five for several years - ups, and still is. That's seven years in a row.
WinZip skipped the number 13 as I just found out. Aahh, winstalgia.