In the past, I've used up to version 7 of winzip on a Pentium 200Mhz. It really should not matter to much what version you use. If a zip program requires more power than what you, then thats just pure bloat.
You may want to consider using 7-zip for zipping your files. It is free, small and fast. Plus can do RAR files.
http://www.7-zip.org/