What I want it to do is to access FBX files in the user's desktop and opens the one the user selects.
"Opening something" does not actually tell us what you want to do.
Open the file with The default application for the file type?
Load the mesh somewhere into RAM?
Spawn objects in UE4 with the mesh?
Who knows what opening means. Opening the file in maya will be quite different from opening it with a hex editor.
Specify what your programm should do.
Shall I open the FBX file using c++ or blueprints?
Appart from what you can add to what I said above this questions answer will be purely subjective if BP is actually capable of doing what you want. IF you are doing good in c++ I suggest to stick with it for file operations.
Here Epics documentation on asset references, this should fit for people finding this thread and probably for you.
https://docs.unrealengine.com/latest/INT/Programming/Assets/ReferencingAssets/index.html
Just use UStaticMesh instead of the filetype used in the examples.
Here a UE4 wiki example implementation of what you could mean:
https://wiki.unrealengine.com/Dynamic_Load_Object