Cross threading in native metal is different than cross threading a threaded insert. The insert is more bendable due to the way it is manufactured. It is more like spring steel. It is the spring tension that holds the insert in place. If you look closely, you will likely see that the threaded insert is bent and not deformed. A thread chaser can only remove damaged threads on native metal, by breaking it off or shaving it. It can't un-bend the threaded insert back into it's original shape and it likely to start unthreading it out of the cyl head. I would examine closely with a 10X glass. As mentioned, if the threaded insert is removed incorrectly, it can damage the outer threads in the cyl head. Also, if it is bent, it will likely grip the chase once you go through the bent area and you may not be able to get the chaser out without pulling the insert and damaging the outer thread. Damage here, will required welding up the hole and re-tapping, if that is even possible and guaranteed to be expensive.
They make tools to properly remove helicoils and this would be the best path for you. It would only take a few minutes for a mechanic with the right tools to do this job safely.
In respect for the previous poster, I agree that a chase can be attempted if the operator is very careful about not letting it get tight or bind. I only fear that someone inexperienced may go too far and get in trouble. I feel it would be easy to get past the point of no return. A good examination of the damage should provide guidance on the likelihood of a chase addressing the issue.
Larry