For whatever menu they will access on whatever desktop environment you are using, there should be a menu editor that allows you to add new entries or edit existing ones.
Which desktop environment/window manager are you using for this on Ubuntu?
By the way, what you are setting up is referred to as
kiosk mode.
This article gives a (likely much too) detailed discussion of kiosk mode.
It sounds to me that all you need is a running session where the users have basically no access to anything other than an icon or menu item for starting the browser. If I'm correct in that, I would recommend that you review the link and consider taking some precautions so users can't access other parts of the machine or do naughty things to your network.