To get around this problem, I have to introduce some development repositories into my installation. This is detailed in this article on installing Avant for Hardy.
It's really quite straightforward. It's just a matter of adding these two lines into the third party repositories of Synaptic:
deb http://ppa.launchpad.net/awn-testing/ubuntu hardy main
deb-src http://ppa.launchpad.net/awn-testing/ubuntu hardy main
After that, the AWN applets package should be available. You will, however, have to uninstall the existing AWN manager as it conflicts with the new packages.