The Check for Updates feature can be disabled by changing the string value NoUpdateChecking from 0 to 1 in HKEY_CURRENT_USER\Software\Nico Mak Computing\WinZip\UpdateCheck
If the same string value change is made in HKEY_LOCAL_MACHINE it will propagate to any new user profiles that may be later added to the same computer.
If you will be installing to other computers in the future, this change can also be configured in the MSI file itself. Please see How do I customize my WinZip MSI?
If you have any questions about this information please email Technical Support.