You might find this difficult and expensive.
The roads between Puerto Montt and Puerto Natales are not good. There is not a paved road that goes the entire distance. What is more, you will have to go into Argentina for part of that trip. Car rental agencies might not want their vehicles traveling those dirt roads. You would be wise to establish contact with a car rental agency before you go to make sure it can be done.
You might consider the ferry between Puerto Montt and Puerto Natales. You're supposed to see some of the best scenery from it. You should be a good sailor to take that trip, however. The ship is not very stable and is famous for causing sea sickness.
You can cobble together some bus transportation in that area, but it takes some planning. There is little regular bus service, but there are some services run by travel agencies.
It is easy to hire a car and driver or take a small bus from Puerto Natales to Punta Arenas. There are lots of them making the trip. There is not much spectacular scenery on that portion of the trip.
Good luck.