How should I implement an alternative file upload?
If you want it to use http://filepicker.io's storage, it will definitely be link field. It's your own design decision if you will just add a widget (that's what I would do) or clone it and add that widget to a clone. However, don't expect seamless work from images on your own domain and images stored away of it - you can't really resize, rotate, crop, generate thumbnails, and service may become paid one with only short notice (and unavailable without any notice at all).