Should a prostitute be reported to the police, knowing that the police will try her according to man-made laws, not Islamic law, and would that be considered aiding in the application of laws that alter the Shari'a of Allah?

Bearing witness in Islam is a grave matter, so it is not permissible for a Muslim to bear witness except to what he is certain of its truth. If you are certain about the state of this woman, then do your utmost to prevent this evil gradually, from admonition to threats, with wisdom and the consultation of people of sound judgment. If that does not work, and reporting to the police prevents the evil, then you must report them out of necessity, because her harm is widespread and her temptation is severe. This is neither an approval nor an acknowledgment of the rule of the taghut.