Companies you should be able to play:
WCPW (Put down as American since you can't do British or European), Border City Wrestling (Canadian Indy Company), Toryumon Mexico, International Wrestling Revolution Group, Etc. to be added soon.
Japanese companies, although you have no control over putting them in as Japanese companies, its best to put them down as regular companies:
DDT Pro, Dradition, Inoki Genome Federation, Dragon Gate, Stardom, Wrestle-1, Real Japan Pro Wrestling, you can find the list here: https://en.wikipedia.org/wiki/List_of_professional_wrestling_promotions