I understand that it can be frustrating to be the wrong background for a production that is trying to be historically accurate especially if you really love the time period, but that is really just part of the genre. Those of us that watch them are already PITAs when it comes to most details they try to get right, to then purposely put in an element that they know isnt accurate.
Lots of white guys would love to be in samurai movies, but outside of really bad ones, like with Tom Cruse, you have to make it in proper context like Shogun in order for it to work.
You can always seek out a fictitious story set in those times (Steampunk pretty much does that), or look for a real person from that time that has an interesting story.
BBC’s Robin Hood 2006-2009 put random Black actors into the series and it didn’t really seem too disturbing. They just played the parts as if it was nothing unusual. Of course, that particular show was based on legend and was more about sword fights and melodrama than historicity.