You could take the back plate off and I'm sure you'll be able to get it out that way. I swapped screens between a silver and blue shell and
posted the steps with photos here that might help you out.
Then you could order another stylus that will fit perfectly in the Sony
from Shapeway here that a member (chris77586) created and set up for us. I've ordered them in the past and they fit perfect. You won't get the slight click or feel of it snapping it place, but it definitely stays snugly inside the channel and will not fall out on its own.
When you slide the stylus out, only push it out the least amount needed to then pull it out. What most make the mistake of doing is pushing against the stylus while sliding it up, and continue that pressure against the stylus when it's no longer needed bending it enough to eventually crack it.
Once you get the stylus out when you remove the back, check if it really is broken or maybe if the top just became unscrewed from the stylus. If you're lucky, that's all that happened and you can just screw it back on. And btw, no part of the stylus is metal, the tip is plastic just colored in silver.