I'm seconding the others here, I kinda wish the dev had stuck with the Evo designs for both Jean Grey and Psylocke.
And while I understand that 616 Psylocke had the weird thing about being British in a British body, being put in an Asian body, then going back to her old one... I vastly prefer the Asian bod. And if we're talking about an alternate universe anyway, I'd go ahead and skip the complicated body switching thing.
I'd just make it so that Betsy is from Hongkong, or at least her mother was. Remember, Hongkong was a British colony some decades ago. It would have been easy for her father (or grandfather) to be from the UK, maybe met someone in Hongkong while doing business there or something.
There are perfectly plausible reasons why Betsy might have a British name and have Asian features. No need to complicate things like the 616 universe did.