What I did was drill into the inside of the mask. You can see the spot you need to drill on the inside. You need to select a drill bit that's slightly smaller than the circumference of the silver portion of the nose. Be very careful to drill straight in, and not to drill at a angle so that you are only drilling through the mask, into the back of the nose "plug." The tricky part is that you actually have to drill much further than you think, there's a lot of material to get through.
After you drill to a certain depth, you will need a tool that will fit into the hole you created. Use something that is flat, not pointed. A pointed too will just pierce into the soft plastic.
This is the scary part. You need to push from the back, till the nose plug pops out of the front of the mask. Depending on how much glue they used on your particular sculpt, this could be very easy or very challenging. Mine took a considerable amount of force, but I've read that it popped out very easily for others. Don't be tempted to try and pry it from the front you will run the risk of slipping and scratching the front of the mask, or deforming the "teeth." Just push from the back. It requires the same steady, firm, but gentle pressure, and of course patience, just like removing the dome and separating the mask.
Once the nose plug is out, just cut it in half, then sand the back side down till its short enough that it looks right. Keep a couple reference images from the film handy as you work. His nose is much deeper into the mask than you might remember.
That's about all the advice I have. I hope it helps. This stuff can be more than a little stressful, but the payoff is SO REWARDING when you look at your completed work.
Matrix did a better job on his nose than I did. Hopefully he can provide some insight into his method.