Let me summarize the requirement - We want to create an emulator for mouse and keyboard that would run on a local PC (Win 10 or Win 10IoT based). This application that you will develop for us and runs on a local PC is connected to the remote PC through 2 USB cables and through those 2 USB cables - one for keyboard and the other for mouse. Through these 2 cables, the local PC can click buttons on the UI of the remote PC or enter text on the UI of the remote PC. So, in essence, your code is acting like a mouse and keyboard for the remote PC. It is not required to show the mouse movement or keyboard cursor, your application can just go to a certain X & Y co-ordinates and perform mouse click or enter text.
Keep in mind that we CAN NOT install any software or hardware on the remote PC and remote PC can be running any OS.