The NY Metropolitan Opera has been offering free streams of past
performances on their website. They will feature Verdi’s “Otello” on 6/6
(Sunday morning in Tokyo, for approximately 24 hours)
https://www.metopera.org/season/on-demand/opera/?upc=811357018026
Maybe not exactly Shakespeare, but close.
PS If the above link doesn’t work, go to this link and click on the
corresponding title:
https://www.metopera.org/user-information/nightly-met-opera-streams/
They usually make the opera of the day around 8:30 AM Tokyo time, and
can be free-streamed for about 24 hours. Before and after that, you’ll
pay $4.99 for the Opera on Demand.