You are on the right track. It is possible to solve the corners of a 4x4x4 cube last.
This tutorial on YouTube, by burgocube, shows how to solve the corners of a 3x3x3 cube. This solution will work for the corners of a 4x4x4 cube too. If you only turn the outer layers of the 4x4, it will act like a 3x3. For example, this is an outer layer turn.
The four centers will be like the one center of a 3x3. Also, two adjacent edges will be like one edge of a 3x3.