On my machine
/bin/sh is a symlink to
dash. All you need is to restore the symlink.
While booted from the LiveCD, mount the root partition somewhere (say,
sudo rm ./sh
sudo ln -s dash ./sh
Something like that.
Update: Regarding "mount the root partition somewhere" - if you booted from a LiveCD and have a full GUI, the easiest would be to open the file browser, in the left pane there will be a few entries one of which correspond to the partition on the hard drive where your Ubuntu is installed (a.k.a "root" partition). Just clicking on the entry mounts the partition and displays its contents. You can tell it's a root partition if you see
var directories there.
When you click on the entry in the file browser's left pane, what's happening behind the scenes is the filesystem is getting mounted as a subtree inside some directory, usually
/media. You can check that using the file browser too.
After you figured out where your partition is mounted at, you open terminal and re-create a symlink.