I believe SUroot recommends winrar on a PC, but I've not used it as I'm not a big Windows user.
I tend to just use Astro on my phone. I found by trial and error that the most reliable way is to multi-select files in the same folder within the zip (e.g. system/app), delete them (which is slow - but perhaps not surprising, if it's actually editing the zip file rather than simply removing a pointer in the filesystem), then use the back button to back out of the zip. Then go back into the zip if I want to delete files from another folder. A bit of a faff, but when I tried just moving around within the zip, deleting files from different folders, many of them would turn out not to be deleted (or not according to Astro). But while it takes a few minutes, this method seems to be reliable (hence my running CM7 nightlies with the Oxygen r2 table - I strip the 86MB zips down to about 50MB before flashing).
Edit: the trick on the computer is just to delete things from the zip, without unzipping it (i.e. do not unzip, delete, re-zip). But I've not used winrar, so can't describe its interface for doing this.