How do I select the source file if context menus aren't available on my system?

You will have to manually open the application, select the files you wish to transfer from an Explorer window, and drag-and-drop them into the application. Do note that when you start the transfer, only the last dropped files will be transferred. This means that if you drag-and-drop files into the application several times without starting the transfer, only the last dropped files will be transferred.