User driverdis at GBATemp has published a full tutorial on how to use a proxy on the Nintendo Switch, which will let you access YouTube and play videos. He mentions that anything requiring to log in (including, but not limited to YouTube Red) will not work.
http://gbatemp.net/threads/tutorial-...ayback.463253/
http://wololo.net/2017/03/08/access-...ideo-playback/
http://wololo.net/2017/03/05/release...omment-4469817
http://gbatemp.net/threads/tutorial-...ayback.463253/
http://wololo.net/2017/03/08/access-...ideo-playback/
http://wololo.net/2017/03/05/release...omment-4469817