This will vary depending on whether you have one of the free versions or Joystix Pro Elite, the paid version.
Joystix Pro Elite
With the paid version, Joystix Pro Elite, you can "Edit" the game's Stik in Stix Studio and once you are at the Editor screen, drag and drop the desktop shortcut icon to anywhere on the Editor screen and hit Save.
Free versions of Joystix Pro
The free versions are a bit trickier and doing so will remove all traces of the free versions of Joystix Pro for your computer. You won't have to re-register, but you will need to re-enter the email address you used when you registered before.
The first thing you need to do is go to Control Panel -> Folder Options and click the "View" tab. Under Advanced Settings, change Hidden files and folders to "Show hidden folders, files, and drives," and un-check "Hide protected operating system files". You may want to leave this window open if you want to change these settings back later.
Next we find the folders. Go to:
C:\Users\<your user name>\AppData\Local\Microsoft
Then delete any file that looks like joystix.exe_Url etc.
To be safe, you can also go one folder up to:
C:\Users\<your user name>\AppData\Local
And then delete any folder that has Blue_Orb in it.
You're done. Go back and change your settings in the Control Panel.