As others have said, building a shelter in the back country should be done in emergencies only. Especially if you are in areas that have high traffic or have rules against it.
That being said, it is good to know how to build a shelter for an emergency, and that takes practice. So, you need to find an area to practice. I have built a few and think it a worthwhile skill to possess. But, you also need to think more realistically. If you are practicing for an emergency, then you need to make it a worthwhile practice. I prefer to do the task without any tools. No knives, axes, saws, or rope. What good is the practice if you might not have the tool you practiced with?
But, for an emergency saw to carry, go with a sierra saw type saw.