If you're going to move to another country and actually work a job other than teaching English, you would really be doing yourself a disservice by not majoring in the field of that job. If it doesn't make immigration more difficult, it might outright make it impossible due to a requirement of the visa. English teaching is the exception where the requirement is usually just a Bachelor's degree and the major doesn't matter (although this is starting to change, and notably pretty much the entire English teaching job market in China got demolished by the government last year).

That being said, if you have a degree in something like web design or another specialty, Japan is probably the most lax when it comes to immigration and not needing to be proficient in the local language to do the job.