I've never tried this, but here is what I think should work.
Get a Knoppix CD and boot it.
Use the tool flash-knoppix to install the system on a stick. That system will be persistent (changes will stick).
Boot from the stick.
Install the uae flavor, Kickstarts and games of your choice.
Configure uae config file.
You can put a line "uae &" into the .xinitrc in the standard user's home folder. UAE will be started automatically.
The problem is that fs-uae and plain uae can't be configured with popup dialogs atm. If you want to start it in full screen mode you will need e-uae or p-uae.