It's been on the forums a few times how to get SQL Developer to put it's config setup on to a flash drive.  The same thing works with Dropbox/Google Drive/...

Here's all it takes.
1) edit sqldeveloper/bin/sqldeveloper.con
   - add the path to the Dropbox or where ever location
    AddVMOption -Duser.home=/Users/klrice/Dropbox/sqldev

2) Start it up.

The to check just look in that location and you'll find a .sqldeveloper directory where everything will be stored.

You'll notice bunches of directories where all the settings are being stored.

Then just go to any machine with your drop box installed and you'll have the exact same setup everywhere.