Hi,
this should be relatively easy to accomplish with Codename One but you will need to do some work.
The Codename One API was based on Swing as a starting point so many of the API's will be instantly familiar to your team e.g. the layout managers are all there and you have List's with renderers etc.
See this basic introduction:
http://www.codenameone.com/swing.htmlIn the past we even recommended people use an AWT GUI builder (not Swing since we don't have J prefix for component names) then change the package imports to get your application to work.
The big things you will need to refactor in your code are:
1. Very complex UI's - you just can't use those on a touch device.
2. JTable - while we have a Table class its far simpler than JTable which is quite hard to adapt conceptually to mobile devices.
3. Frames/Dialogs - we have Forms and Dialogs which are a bit different, naturally you don't open many Windows at once.
4. Desktopish concepts - tooltips, context menus etc. don't make much sense here.