If the goal is to have the output be compatible with pkzip and winzip, I'm not aware of any open source libraries that do this. We had a similar requirement for one of our apps, and I wound up writing our own implementation (compatible with the zip standard). If I recall, the hardest thing for us was that we had to generate the individual files on the fly (the way that most zip utilities work is they create the big zip file, then go back and split it later - that's a lot easier to implement. Took about a day to write and 2 days to debug.
The zip standard explains what the file format has to look like. If you aren't afraid of rolling up your sleeves a bit, this is definitely doable. You do have to implement a zip file generator yourself, but you can use Java's Deflator class to generate the segment streams for the compressed data. You'll have to generate the file and section headers yourself, but they are just bytes - nothing too hard once you dive in.
Here's the zip specification - section K has the info you are looking for specifically, but you'll need to read A, B, C and F as well. If you are dealing with really big files (We were), you'll have to get into the Zip64 stuff as well - but for 24 MB, you are fine.
If you want to dive in and try it - if you run into questions, post back and I'll see if I can provide some pointers.