So as people have told you, the PS4 has its own recording software. I don't know how it really works, but I doubt it will allow you to export to your PC. Even if it doesn't, however, uploading to youtube is good enough if you have a good cap-less internet connection. You could upload the video to youtube as private and then use one of the million tools there are to download videos of youtube. Download your own video from Youtube, edit it and reupload. It would be a hassle, but it could work if there's no alternative... but we still don't really know anything about the PS4's recording software.
Yes I have also thought about this way, but the quality wont be as good as when capturing directly though :/