If you want to develop your own asset format, then you will have to implement all the functions like "D3DXLoadHierarchyMeshFromX", which DirectX provides for meshes.
It would be better to first understand what exactly your engine can use (or does use) from the .X file. For example, I am in the process of developing an engine and I have defined a simple binary format, using which I load my meshes. As right now I am not doing any animations, so I have not updated my mesh converter to include animation data in the end format.
You will have to understand your engine's exact requirements and probably make an asset converter, which can convert your assets from formats like .fbx to your proprietary format. You may have to make a lot of changes in your asset loading module.
So, you may not require a lot of changes in your engine, but at least the loading mechanism has to be changed. Still, without knowing how you have implemented your engine, I can only speculate.