I have an (unsigned) applet that let you draw a logic circuit and test it on-screen (a bit like Electronics Workbench), and it then serializes the circuit (the internal form
(Which sounds like it means "Future updates will deny the execution of Java applications" -- unless you pay money to Thwaite or Verisign on a regular basis AND expose users to code running outside a sandbox.)
A signed applet launched using JNLP can still be sand-boxed.
But if you really wish to avoid it..
I think what you described can be provided using JavaScript for the logic and and an HTML 5 canvas for the rendering.
I would avoid Flash, since it is also susceptible to security bugs. It would be like digging yourself a brand new hole to get trapped in.