Here are the complete instructions for my future self and those interested.
The solution is to install firefox 32 bits with Oracle Java 32 bits.
First get firefox 32 bits:
wget http://ftp.mozilla.org/pub/mozilla.org/firefox/releases/latest/linux-i686/en-US/firefox-27.0.1.tar.bz2
bunzip2 firefox-27.0.1.tar.bz2
tar -xvf firefox-27.0.1.tar
Then get Oracle java 32 bits (replace download with latest version):
wget --no-cookies --header "Cookie: gpw_e24=http%3A%2F%2Fwww.oracle.com" "http://download.oracle.com/otn-pub/java/jdk/7u51-b13/jre-7u51-linux-i586.tar.gz"
tar -xzvf jre-7u51-linux-i586.tar.gz
mkdir /usr/local/java
sudo mv jre1.7.0_51 /usr/local/java
Create and activate the alternative for the java plugin into firefox:
sudo update-alternatives --install "/usr/lib/mozilla/plugins/libjavaplugin.so" "mozilla-javaplugin.so" "/usr/local/java/jre1.7.0_51/lib/i386/libnpjp2.so" 1
sudo update-alternatives --set "mozilla-javaplugin.so" "/usr/local/java/jre1.7.0_51/lib/i386/libnpjp2.so"
Shut down all instances of Firefox if already running, and start 32 bits firefox:
cd ~/firefox
./firefox
To check the version of java, type about:plugins
in the address bar.
It should display:
Java(TM) Plug-in 10.51.2
File: libnpjp2.so
Path: /usr/local/java/jre1.7.0_51/lib/i386/libnpjp2.so
Version: 10.51.2
State: Enabled
Next Generation Java Plug-in 10.51.2 for Mozilla browsers
Note that when you are done with Webex, you can change back your version of the java plugin to the 64 bit version (if it was installed) by typing:
sudo update-alternatives --config "mozilla-javaplugin.so"
And selecting the correct entry.
Additionally, it is necessary to install missing webex libraries as described in Russ Lowenthal's answer:
cd ~/.webex
ldd *.so | grep "not found"
#get the package containing the missing libraries (example libXtst.so.6):
dpkg -S libXtst.so.6
#install the corresponding package (appending i386 for the 32bits version)
sudo apt-get install libxtst6:i386
Tested also on a fresh install of Ubuntu 14.04 Trusty Tahr, it works.
Let me know if you have problems.