The cursor is just for display. Hiding the default cursor and drawing your own one won't affect the move and click.
I guess there are two possibilities what you are doing:
If you just want to display a custom cursor, you should just hide the system cursor when the mouse is inside your window. So the user knows what he/she is doing when the cursor is outside your window. Or you can constrain the mouse inside your window with ClipMouse.
If you are handling the mouse completely by yourself with something like DirectInput, again, you should use ClipMouse.