From the Start menu's Run dialog, enter this command:
regsvr32 /u zipfldr.dll.
Repeat and enter:
regsvr32 /u cabview.dll.
Each time, you should get a notice that
DllUnregistersucceeded. Contrary to numerous Web sites displaying this advice, you need to restart the computer for the change to take effect.
I've gotten different advice over the years, and have instructions at home that I know work, but hopefully this does as well (still need to reboot)...
UPDATE: Turns out this didn't work for me, so need to dig up my info at home
UPDATE2: The hint from Mike works. Run
regsvr32 /u zipfldr.dll, reboot straight away, then run WinZIP immediately and answer yes to "fully associate ZIP files with WinZip??". Confirmed that it works because search now doesn't look through ZIP files.