I tend to remember an auto-mount option for partitions in Classic's Drive setup. Without rebooting I cannot check. If you turn this flag off the Finder should not see the partition but will the kernel?
As far as I know, the Finder shows any drive or partition that is mounted. Unfortunately, this means you also need to mount the swap partition. The Finder, and also Open and Save dialogues, use a ".hidden" file to tell it what not to show. The only one I know of is kept at the root of your main partition. Feasibly, you just need to create a .hidden file with the name of the volume you are thinking of in the Volumes folder. Just su to root, and type
cd /Volumes;echo "Odysseus" > ".hidden"
This will create the file. However, I think there will also be some ownership problems, so someone else will have to suggest what to do for that (I don't have access to my computer right now).