If you use Windows, you can get a directory listing via old-school way in Command Prompt.

Copy your stuff about to be zipped to some place, like D:temp 

Fire up Command Prompt (in Accessories or with 'Run', putting in cmd as the program you want to run), and then navigate to the right directory with cd and other archaic commands; using my example, you'd have to type d: and then cd temp.

Finally, in the example directory of temp,  dir /b /s > contents.txt

Voilá! Bob's your uncle.

There are also small utility apps that do this for you, if you feel more visual. IIRC some zipping programs can do it as well.