Use swap for hibernating only
I won't copy and paste the entire article, but I think this is what you want:
- How to use hibernation without a swap partition
- Setting Up Hibernation on Linux SSD Netbooks Without Swap
The first link is a succinct Debian article which should be close enough to get it working on Ubuntu. The second is an article using Kubuntu which should be closer to home but it looks like the same process as the Debian link just spanned over five pages with a bunch of fluff in between.
Pick your poison. :)