I had that very same problem ....
I grabbed a very thin screwdriver, heated it up almost to red, and with plenty of light, and very carefully, I inserted it into the stylus cavity .... when I reached the broken part, I made some force, penetrating the plastic of the stylus... I waited a bit for it to cool off, and pulled it out.
It seems dangerous but I realized also that the plastic melting point of the zaurus is higher than the stylus. That is, you MIGHT touch the inside of the zaurus, for a split second, but chances are that you are not deforming it. Your AIM must be good tho