I see you're asking this of Simone, but I hope you don't mind if I weigh in with an answer too.
If you have any control over the speech topic then make sure it is something you are very familiar with:
For example, if you were told to give an impromptu speech on a personal topic, you may feel awkward. However, if the impromptu speech was about programming languages your awkwardness may start to take a backseat to your knowledge.
Next, I identify your "crutch" word:
For awhile I did computer training for pharmaceutical reps, sometimes groups up to 50 at a time. So I was very aware that my crutch word was "ok" and it was so much easier to catch myself saying it when I practiced, when I knew what it was. All I had to do was replace "ok" with silence, which became easier to do the more I practiced.
Clearly, the more you are prepared, the more your knowledge outshines your awkwardness and the easier it becomes to avoid using a crutch word. So practice a ton and practice standing up.
All that being said, you can't change who you are. If you are socially awkward, then own it. If you focus on changing it for a few minutes for your speech you will probably just feel anxious. You are who you are. People come in all different types of personalities, and how bland and boring would it be if every speech giver was a carbon copy of each other. That is not what your professors expect. But practice, practice, practice.