Is it permissible for me to shorten the prayer (qasr) in North Sinai, given that I am a soldier stationed there for more than forty days, and I am not from its people and consider myself to be traveling?

As long as you are staying four days or more, it is not permissible for you to avail yourself of the concessions of travel, such as shortening prayers and breaking the fast in Ramadan. For among the conditions for availing oneself of these concessions is that the journey must not be for the purpose of disobeying Allah the Almighty.