If the installer is running as admin and your AutoIt script is running as a standard user then automation issues may occur.
Add this directive to the top of the script to run the script as admin.
Add this directive to the top of the script to run a compiled script as admin. This adds the require admin to the resources of the executable.
#pragma compile(ExecLevel, requireAdministrator)
Have a look in the AutoIt help file for Tutorials > WinZip Installation. If you can follow that tutorial then perhaps you can progress to using the Control* functions. Looks like the latest WinZip is about 10 versions higher then the tutorial version so some subtle differences may exist. If you have further issues with your attempts, then post your attempts and help may follow.
Also have a look at the pinned topic of AutoIT Script Collection for some examples.