I agree with Tim- stabilizing the piece makes working on it much better in many ways.
The method I use is to insert the nozzle into a metal rod that I have clamped in my vise. This keeps the horn in place and allows you to turn it as you work on it. (I have not had any issues with this method for the near sixty horns I’ve made this way) - keep the nozzle a bit fat and it handles the strain- I thin it down after all the heavy rasping and filing is done.
Good luck on your horn project nonetheless- it’s very cool to make your own.